Pretty good summary, but a couple of clarifications.
The Imperium is usually described as having a million worlds, and in some sources it's stated to have millions of worlds. Either way, a bare minimum of one million is pretty safe to say, with their territory stretching across 90,000 light years in the Milky Way galaxy.
According to the 3rd edition rulebook, 100 billion is the minimum. Hive Worlds have populations ranging from 100-500 billion. And according to the 5th edition rulebook, the Imperium has about 32,380 of them.
Trust me, Imperial ships aren't in danger of falling apart. These're ships that are capable of surviving thousands of years of service. They're very tough.
Outclassed in what way? Maneuverability is about all a Starfleet vessel has over them, but that's to be expected from something vastly smaller. In nearly every other way an Imperial vessel is superior. It's larger, has far more firepower, its weapons can inflict levels of devastation which make the weapons on a Starfleet ship pale in comparison, has shields and hull plating that can resist similar firepower in return, and its FTL is massively superior. Sure, they don't got astrometrics labs aboard, but who needs 'em?
They'd be a bit superior. They do wear body armor, after all, but then again we're talking phasers. So it depends how far you turn up the dial on the phasers, but their body armor could probably resist the low settings. More importantly, though, the Imperial troops are armed with automatic energy weapons that can lay down a veritable hail of fire. That outclasses the one-shot phaser, no matter how powerful each individual shot is.
And to top it off, most Imperial troops hail from insanely violent worlds like Hive Worlds, Feral Worlds, and Death Worlds. So those Imperial troopers, even the standard ones, have probably experienced far more horror and bloodshed than any Starfleet Officer has seen in his whole life, and that was before they joined the Guard! An Imperial soldier is just as likely to hail from a feral world, in which case he may end up scalping you, or may be a headhunter.
Yeah. The lesser guns on some Imperial ships are the size of a Sovereign, alone, and they have several guns that're just as big. Imperial torpedoes on the cruisers and battleships are 1/10th to 1/7th the length of the Sovereign Class. And from calculations done by others based off of evidence in the books, the weaponry has a power output in the terraton to petaton range. Even the smallest and weakest ship in the Imperial Navy, the Cobra Class Destroyer, is still something in the neighborhood of 5 times bigger than the Sovereign.
Although when it comes to Imperial technology, it varies. A lot of their stuff is left over from previous ages, but they've still got some pretty amazing tech. For instance, they've got access to technology allowing their weapons to bypass shields. One novel has a ship firing a torpedo which completely bypasses the shields of a target (no idea of the commonality of this device, but given that torpedoes can bypass shields entirely...). This technology is even miniaturized so much that they can put it on a special brand of bullet for their assassins.
They have a drug callled polymorphine which allows for rapid shapechanging, allowing for far greater infiltration than the simple surgical alterations performed by Starfleet. They have access to vortex weaponry, which literally splits a hole in reality, utterly destroying anything within the blast radius of the weapon. You'll find these weapons aboard ships, titans, and you'll even find them in the hands of Imperial agents (vortex grenades!).
The Imperium also has personal force field technology, and you'll find all their most important commanders and field leaders protected by one kind of personal force field or another. One of the most impressive being the displacer field, which is a miniatured warp drive and a proximity sensor. When it detects incoming projectiles, it literally warps you out of the way.
Not to mention body armor and power armor, none of which the Federation uses. As well as power weapons and power fists (giant mechanical gauntlets granting the wearer superhuman strength). Jump packs for rapid transportation. Nevermind force weaponry which their psykers make great use of.
And of course, their FTL is vastly superior (if unreliable, but that's a result of the environment they travel through and not a deficiency of the FTL system, itself. If warp space were more calm, warp travel would be more reliable). A standard Imperial ship can travel 10,000 light years in 10-40 days. That's likely just a transport. A Space Marine ship, for example, can travel much faster then that.
By way of comparison, if an Imperial ship had been kidnapped by the Caretaker and found itself 70,000 light years from where it started, it would've only taken 70-280 days to get back. Not the 60+ years that it would've taken Voyager. The Federation is 8,000 light years across, so an Imperial ship can cross the entire span of the Federation in 8-32 days.
Those are just some examples of ways that Imperial technology surpasses Federation technology. Don't let simplistic weapons like the lasgun fool you. They're much more sophisticated then they appear. They just prefer to use lower tech tools because A) they're cheaper, B) they're easier to mass produce, C) they're easier to repair and/or replace in the field, and D) they're much more durable than more advanced items, which're also conversely more delicate.
The lasgun, despite its simplicity, can literally be taken into any environment, abused by the rigors of war, and it'll continue functioning. It's simple enough that enough a primitive savage from a backwater world can learn to use and maintain it. And it can even be charged by leaving its power cells out in the open, where they're charged by solar power, or by even putting the batteries inside a fire! And to top it off, it serves well enough as a tool of war, ably killing most of the enemies Imperial troops come across. Is a phaser better? In most ways, sure. But for all the reasons listed above and more, the lasgun is a better tool of war, which is why the Imperium favors it (and frankly, the Federation troopers at the Siege of AR-558 would've done much better armed with lasguns than phaser rifles. What's the point of having a weapon that can melt a rockface when the situation calls for a weapon that will still kill the enemy while putting out a greater fussilade of fire? And the lasgun, an automatic weapon with easily replaceable ammo, is that weapon).
The only question is, how would they even get inside the hull? Imperial torpedoes are designed to penetrate some distance into a hull before detonating, but a Starfleet torpedo? It's clearly designed to impact on the hull. And the hulls on Imperial ships, even without shields, or able to withstand terratons of firepower. Maybe more. So while they could inflict some damage over time, it wouldn't be fast enough. What Starfleet would need, aside from a vastly more powerful torpedo then what's seen in canon, and getting lucky in finding an unshielded Imperial ship, is a torpedo which is designed to penetrate through a hull, first, before going off. Not an easy feat, though, when you're talking about a meters thick hull composed of adamantium.
The Imperium of Man consists of hundreds of thousands of inhabited worlds
The Imperium is usually described as having a million worlds, and in some sources it's stated to have millions of worlds. Either way, a bare minimum of one million is pretty safe to say, with their territory stretching across 90,000 light years in the Milky Way galaxy.
and some of them are called Hive Worlds that contain up to a hundred billion people.
According to the 3rd edition rulebook, 100 billion is the minimum. Hive Worlds have populations ranging from 100-500 billion. And according to the 5th edition rulebook, the Imperium has about 32,380 of them.
but they are in constant danger of just falling apart.
Trust me, Imperial ships aren't in danger of falling apart. These're ships that are capable of surviving thousands of years of service. They're very tough.
and for sure very outclassed by Starfleet vessels. However they are heavily armored and shielded and did i mention big so one needs to inflict quite some damage to really affect them.
Outclassed in what way? Maneuverability is about all a Starfleet vessel has over them, but that's to be expected from something vastly smaller. In nearly every other way an Imperial vessel is superior. It's larger, has far more firepower, its weapons can inflict levels of devastation which make the weapons on a Starfleet ship pale in comparison, has shields and hull plating that can resist similar firepower in return, and its FTL is massively superior. Sure, they don't got astrometrics labs aboard, but who needs 'em?

Another thing to take into consideration are boarding actions.. if done by "normal" imperial Navy personell then they'd be not that different to Starfleet personell. Maybe leaning a bit more to the true military but they'd be a match for Starfleet (Starfleet officers rarely wear any kind of body armor).
They'd be a bit superior. They do wear body armor, after all, but then again we're talking phasers. So it depends how far you turn up the dial on the phasers, but their body armor could probably resist the low settings. More importantly, though, the Imperial troops are armed with automatic energy weapons that can lay down a veritable hail of fire. That outclasses the one-shot phaser, no matter how powerful each individual shot is.
And to top it off, most Imperial troops hail from insanely violent worlds like Hive Worlds, Feral Worlds, and Death Worlds. So those Imperial troopers, even the standard ones, have probably experienced far more horror and bloodshed than any Starfleet Officer has seen in his whole life, and that was before they joined the Guard! An Imperial soldier is just as likely to hail from a feral world, in which case he may end up scalping you, or may be a headhunter.
Sure the imperial technology sucks in comparison to Starfleet but a single direct hit by an imperial weapons battery or a lance battery (huge, honkin' superlaser) would instantly destroy even a Sovereign class.
Yeah. The lesser guns on some Imperial ships are the size of a Sovereign, alone, and they have several guns that're just as big. Imperial torpedoes on the cruisers and battleships are 1/10th to 1/7th the length of the Sovereign Class. And from calculations done by others based off of evidence in the books, the weaponry has a power output in the terraton to petaton range. Even the smallest and weakest ship in the Imperial Navy, the Cobra Class Destroyer, is still something in the neighborhood of 5 times bigger than the Sovereign.
Although when it comes to Imperial technology, it varies. A lot of their stuff is left over from previous ages, but they've still got some pretty amazing tech. For instance, they've got access to technology allowing their weapons to bypass shields. One novel has a ship firing a torpedo which completely bypasses the shields of a target (no idea of the commonality of this device, but given that torpedoes can bypass shields entirely...). This technology is even miniaturized so much that they can put it on a special brand of bullet for their assassins.
They have a drug callled polymorphine which allows for rapid shapechanging, allowing for far greater infiltration than the simple surgical alterations performed by Starfleet. They have access to vortex weaponry, which literally splits a hole in reality, utterly destroying anything within the blast radius of the weapon. You'll find these weapons aboard ships, titans, and you'll even find them in the hands of Imperial agents (vortex grenades!).
The Imperium also has personal force field technology, and you'll find all their most important commanders and field leaders protected by one kind of personal force field or another. One of the most impressive being the displacer field, which is a miniatured warp drive and a proximity sensor. When it detects incoming projectiles, it literally warps you out of the way.
Not to mention body armor and power armor, none of which the Federation uses. As well as power weapons and power fists (giant mechanical gauntlets granting the wearer superhuman strength). Jump packs for rapid transportation. Nevermind force weaponry which their psykers make great use of.
And of course, their FTL is vastly superior (if unreliable, but that's a result of the environment they travel through and not a deficiency of the FTL system, itself. If warp space were more calm, warp travel would be more reliable). A standard Imperial ship can travel 10,000 light years in 10-40 days. That's likely just a transport. A Space Marine ship, for example, can travel much faster then that.
By way of comparison, if an Imperial ship had been kidnapped by the Caretaker and found itself 70,000 light years from where it started, it would've only taken 70-280 days to get back. Not the 60+ years that it would've taken Voyager. The Federation is 8,000 light years across, so an Imperial ship can cross the entire span of the Federation in 8-32 days.
Those are just some examples of ways that Imperial technology surpasses Federation technology. Don't let simplistic weapons like the lasgun fool you. They're much more sophisticated then they appear. They just prefer to use lower tech tools because A) they're cheaper, B) they're easier to mass produce, C) they're easier to repair and/or replace in the field, and D) they're much more durable than more advanced items, which're also conversely more delicate.
The lasgun, despite its simplicity, can literally be taken into any environment, abused by the rigors of war, and it'll continue functioning. It's simple enough that enough a primitive savage from a backwater world can learn to use and maintain it. And it can even be charged by leaving its power cells out in the open, where they're charged by solar power, or by even putting the batteries inside a fire! And to top it off, it serves well enough as a tool of war, ably killing most of the enemies Imperial troops come across. Is a phaser better? In most ways, sure. But for all the reasons listed above and more, the lasgun is a better tool of war, which is why the Imperium favors it (and frankly, the Federation troopers at the Siege of AR-558 would've done much better armed with lasguns than phaser rifles. What's the point of having a weapon that can melt a rockface when the situation calls for a weapon that will still kill the enemy while putting out a greater fussilade of fire? And the lasgun, an automatic weapon with easily replaceable ammo, is that weapon).
If we are going the realism route then Starfleet torpedoes should have been vastly more powerful than depicted in the shows.. they contain warheads that are vastly more powerful than any nuclear bomb and should some of them detonate inside an imperial ship then even they stand no chance
The only question is, how would they even get inside the hull? Imperial torpedoes are designed to penetrate some distance into a hull before detonating, but a Starfleet torpedo? It's clearly designed to impact on the hull. And the hulls on Imperial ships, even without shields, or able to withstand terratons of firepower. Maybe more. So while they could inflict some damage over time, it wouldn't be fast enough. What Starfleet would need, aside from a vastly more powerful torpedo then what's seen in canon, and getting lucky in finding an unshielded Imperial ship, is a torpedo which is designed to penetrate through a hull, first, before going off. Not an easy feat, though, when you're talking about a meters thick hull composed of adamantium.