We can thank Jeph Loeb for Mongal's name. She died a few years ago, so it's no longer much of an issue in the comics (though a few people are betting that since it was Mongul II who killed her, she'll be back as a Black Lantern).
I'm not familiar with War World's pre-crisis history, but I do know the first time we saw Mongul I post-crisis, he was already installed as the ruler of War World, which is a giant metal planet, similar to the Death Star, though not intended to destroy planets. Mongul would go around the universe searching for the best fighters and putting them in gladatorial games to the death.
After the events of something that is way too convoluted to get into here, Superman needed to take some time off from Earth and headed out into space. He was eventually knocked unconscious and found by some of War World's scouts. They quickly brought him on board and made him fight. He kept refusing to kill, which upset Mongul, as it also inspired the people of War World. Mongul arranged for Superman to fight his toughest warrior, Draaga. Again, Superman refused to kill and ended up fighting Mongul and winning.
Mongul was deposed and eventually Brainiac found War World and took control. He used it to attack Earth during the "Panic in the Sky Crossover" and lost, when the heroes of Earth (aided by Draaga, who sacrificed himself during the battle) fought back. War World was turned over to the people and was destroyed at some point later on (not sure when).
Mongul, vowing revenge on Superman, attempted to reclaim War World. However, Hank Henshaw, (a poor man's Reed Richards, whose crew died as a result of their exposure to cosmic radiation, and who, was thought dead himself, until he manifested the ability to inhabit machinery) found Mongul and the two launched a plan to defeat Superman and rebuild Coast City.
Because Superman at this time was "dead" following his fight with Doomsday, Henshaw used some Kryptonian technology he found and Superman's DNA to create a new body for himself, and became the Cyborg Superman (one of the four Supermen during "Reign of the Supermen.").
He garnered the trust of the people and the President and used this trust to hide the fact that Mongul had arrived. With Mongul's arrival and Henshaw's mastery of machines, they launched a plan to turn Earth into War World. Coast City, home of Hal Jordan, was destroyed and turned into "Engine City," the first of what were to be many such cities designed to launch the new War World through space.
The real Superman, having returned, along with the other three Supermen and Hal defeated Mongul and the Cyborg Superman. Of course, this is the event that lead Hal to become Parallax, but that's another story.
Mongul was stranded on Earth and eventually killed by Neron.
However, we later learned that Mongul had children when Mongul II came looking to train Superman to help him defeat Imperiex. Imperiex sought to wipe out Earth and the entire Multiverse as a part of the natural order of things. Mongul was later joined by his sister, Mongal, along with a contingency of alien races hoping to defeat Imperiex.
However, Brainiac's descendent, Brainiac 13 turned Pluto into another War World to stop Imperiex. Both villains were defeated and somehow, Pluto was restored, but later suffered the shame of being demoted to dwarf planet.
Mongul visited Earth again to try to cultivate the Black Mercy, plants that put their victims into comas while inducing a dreamlike version of their heart's desire. Green Lantern and Green Arrow defeated him, causing him to go home, where he promptly killed Mongal.
Lately he's gotten possession of a Sinestro Ring and battled it out with the Green Lantern Corps, wherein they found the mother of the Black Mercy's after Mongul tried to turn her spawn into plants that induced fear into its victims. The mother of the Black Mercy's had to choose between the Sinestro Corps and the Green Lantern Corps, choosing the latter. Mongul was defeated, had an arm ripped off, and was presumed dead, but snuck off to take over Daxam and try to wrest control of the Sinestro Corps from Sinestro himself. The two are set to meet during "The Blackest Night" crossover starting next month.
And that's the post-crisis history of War World and the two men called Mongul.
