Most of your questions have been answered already, but let me chime in with my own story of hatred for the Sword and Sorcery Gamma World:
It blows.
One of my very first RPGs was Gamma World. That was back in 1981, when most of you young punks weren't even born yet. [Starts sniffing, takes out hankie, wipes tears of nostalgia away] Every time I see that black-and-white picture of the Buck Rogers dudes approaching the ruined city, I get all misty-eyed.
Fast forward to 2003. I was one of the first in line at my FLGS to buy the "new" Gamma World from Sword and Sorcery. After finding over two dozen typos in the first three chapters and marvelling at the awkward mechanics (the game uses D20 Modern but the authors didn't really understand *how* to use D20 Modern...their added-on psionics system, for example, is dreadful) I promptly sold my copy. Never looked back.
Oh, and the Alternity version of Gamma World is interesting, but not really Gamma World. There are no rules for playing a mutated animal, and only humans can use advanced technology, and the nuclear holocaust was started by aliens (!) . . .
If you *really* want to play Gamma World, buy D20 Modern and D20 Future. That's all you need, baby. One of the campaign settings in D20 Future is, essentially, Gamma World with the numbers filed off. Obviously WotC was disappointed at how Sword & Sorcery butchered Gamma World and tried to make it right, albeit in a small way...
Omega World is great, but far too comical to be Gamma World. In my view, it's more of a parody of Gamma World. And a good one, at that. Worth picking up if you can find that back issue of Dungeon that features it.