Here's my speculation. Don't take it as canon. Let's have some fun.
People who watch DS9 wrote speculations of Odo being hollow inside(wish I could remember where), but that just doesn't make sense to me. If he was hollow inside, he'd dent in and regain his shape like memory foam if you squeezed his arm hard enough or punched him in the stomach. I didn't see his skin or hair get shoved inward when he got smacked in the head by rocks in Vortex. I do recall the statement "you're heavier than you look!" This is because things that are full of fluid tend to be heavy.
I think Odo is "solid" on the surface as much as necessary to mimic skin, eyes, fingernails, clothes, etc. But I think on the inside he's more like gelatin.
What I imagine Odo's interior is like...
He's got a very basic esophagus(according to the Star Trek Encyclopedia) which is why he can't eat or drink. Maybe food falls right through him. Maybe the fluids he tries to drink just circulate right back out as foreign material. Maybe Odo can't swallow at all, period, so he ends up spitting stuff back out. Swallowing takes muscles and reflexes, both of which he lacks. He is only humanoid on the surface. Inside, he has no heart, lungs, spleen, liver, kidneys, intestines, bones, etc. (Yes folks, that means he doesn't pee or poop!)
Now, we get to the episode Facets. I believe Curzon!Odo bypassed Odo's lack of internal organs because having Curzon in his head let Odo form organs he didn't normally have(this happened when his physical appearance changed), and Curzon's consciousness gave him a sense of taste and the ability to eat and drink. This all went away once Curzon left, but Odo remembered tasting everything Curzon ate and drank. (I'd hate to imagine the mess after Curzon left. All that undigested matter! Eww! Poor Odo.)
I think Odo does have a rudimentary airway leading to air sacs that let him take in air for speech. There is no gas exchange. They're basically balloons, nothing more. Odo can't die from a lack of oxygen because his species doesn't need it to survive.
It's been shown in closeups that Odo's chest rises and falls like ours. (Mostly due to Rene needing to breathe, but let's have fun with it!) Maybe Odo "breathes" to keep his internal temperature closer to what's optimal for shape shifting in warmer environments. In cooler environments, he can circulate his inner substance at high speeds to keep himself warm since he can't shiver like humanoids if he's cold. (It IS stated in canon that there is an optimal temperature for shape shifting!) Since he doesn't have a diaphragm, I imagine he has just one low-density hollow in his chest to house the air sacs. The density of his chest wall decreases to suck air in and increases to push it back out. He has complete control of this, there is no reflex. But while he consciously breathes, he doesn't think about it much, just like we don't think about our own breathing unless attention is called to it. (And while he can stop if he wants and not feel any urgent desire to breathe, our bodies will force us to take in air eventually!)
Another question people ask is if Odo has private parts. He shape shifted what he needs well enough if Arissa couldn't tell it was his first time in A Simple Investigation. I imagine his brief time stuck as a humanoid let him "explore" a little... >_>;;
Now for the jello part!
Every time a Changeling takes humanoid form, they build themselves into a gelatinous, vaguely humanoid shape before the skin and such appears. If this surface is disturbed enough, it reveals the gooey stuff underneath. These pictures are what tells me the skin is only a surface facsimile covering a jelly-like interior.
Here's the female Founder taking humanoid form. Her shape is female by her choice and not because of specific gender identity. Maybe she thought a female body would be less threatening.
Odo "gets naked" for Kira by literally letting his surface disappear to show his liquid interior before he turns into glowing fog.
More instances of gelatinous material being visible. The first image is a prime example showing us he's a jello mold behind his imitated skin!
So, as you can see, I think Odo and the Founders are walking, talking, intelligent jello molds while in humanoid form.
A humanoid form is pretty complicated. We've got all those folds and dimples and hairs and pimples and...JUST SO MUCH STUFF!
Objects are probably easier to shape shift into more precisely, but I'll be here all night trying to write that down.
tl;dr version: ODO IS JELLO.
People who watch DS9 wrote speculations of Odo being hollow inside(wish I could remember where), but that just doesn't make sense to me. If he was hollow inside, he'd dent in and regain his shape like memory foam if you squeezed his arm hard enough or punched him in the stomach. I didn't see his skin or hair get shoved inward when he got smacked in the head by rocks in Vortex. I do recall the statement "you're heavier than you look!" This is because things that are full of fluid tend to be heavy.
I think Odo is "solid" on the surface as much as necessary to mimic skin, eyes, fingernails, clothes, etc. But I think on the inside he's more like gelatin.
What I imagine Odo's interior is like...
He's got a very basic esophagus(according to the Star Trek Encyclopedia) which is why he can't eat or drink. Maybe food falls right through him. Maybe the fluids he tries to drink just circulate right back out as foreign material. Maybe Odo can't swallow at all, period, so he ends up spitting stuff back out. Swallowing takes muscles and reflexes, both of which he lacks. He is only humanoid on the surface. Inside, he has no heart, lungs, spleen, liver, kidneys, intestines, bones, etc. (Yes folks, that means he doesn't pee or poop!)
Now, we get to the episode Facets. I believe Curzon!Odo bypassed Odo's lack of internal organs because having Curzon in his head let Odo form organs he didn't normally have(this happened when his physical appearance changed), and Curzon's consciousness gave him a sense of taste and the ability to eat and drink. This all went away once Curzon left, but Odo remembered tasting everything Curzon ate and drank. (I'd hate to imagine the mess after Curzon left. All that undigested matter! Eww! Poor Odo.)
I think Odo does have a rudimentary airway leading to air sacs that let him take in air for speech. There is no gas exchange. They're basically balloons, nothing more. Odo can't die from a lack of oxygen because his species doesn't need it to survive.
It's been shown in closeups that Odo's chest rises and falls like ours. (Mostly due to Rene needing to breathe, but let's have fun with it!) Maybe Odo "breathes" to keep his internal temperature closer to what's optimal for shape shifting in warmer environments. In cooler environments, he can circulate his inner substance at high speeds to keep himself warm since he can't shiver like humanoids if he's cold. (It IS stated in canon that there is an optimal temperature for shape shifting!) Since he doesn't have a diaphragm, I imagine he has just one low-density hollow in his chest to house the air sacs. The density of his chest wall decreases to suck air in and increases to push it back out. He has complete control of this, there is no reflex. But while he consciously breathes, he doesn't think about it much, just like we don't think about our own breathing unless attention is called to it. (And while he can stop if he wants and not feel any urgent desire to breathe, our bodies will force us to take in air eventually!)
Another question people ask is if Odo has private parts. He shape shifted what he needs well enough if Arissa couldn't tell it was his first time in A Simple Investigation. I imagine his brief time stuck as a humanoid let him "explore" a little... >_>;;
Now for the jello part!
Every time a Changeling takes humanoid form, they build themselves into a gelatinous, vaguely humanoid shape before the skin and such appears. If this surface is disturbed enough, it reveals the gooey stuff underneath. These pictures are what tells me the skin is only a surface facsimile covering a jelly-like interior.
Here's the female Founder taking humanoid form. Her shape is female by her choice and not because of specific gender identity. Maybe she thought a female body would be less threatening.
Odo "gets naked" for Kira by literally letting his surface disappear to show his liquid interior before he turns into glowing fog.
More instances of gelatinous material being visible. The first image is a prime example showing us he's a jello mold behind his imitated skin!
So, as you can see, I think Odo and the Founders are walking, talking, intelligent jello molds while in humanoid form.
A humanoid form is pretty complicated. We've got all those folds and dimples and hairs and pimples and...JUST SO MUCH STUFF!
Objects are probably easier to shape shift into more precisely, but I'll be here all night trying to write that down.
tl;dr version: ODO IS JELLO.
"Ugh. Forget it. Just flush what's left of me and get it over with." 
