Red Superfly
You creepy little stalker
When Vader and Emperor die, it's over. Simple as that.
Suspend belief and just be safe in the knowledge that Lucas doesn't care too much about post ROTJ stuff. As far as the OFFICIAL timeline goes, the baddies are gone. End of story.
No Empire, Republic would just resume command under The Republic again surely? Those that were in the Rebellion and Galactic Senate would pick up the pieces.
The Stormtroopers/clones I have no idea how they would be integrated into society due to the lack of any need for a grand army anymore. We still don't know how many clones are still in the Stormtroopers, and how many of them are still Jango clones. We don't know if Stormtroopers still use the Jango blueprint by that time, or if the officer preference thing has taken over completely in the Stormtrooper ranks. Maybe the troops would re-integrate back into society as normal, or maybe they could branch off and become a renegade, leaderless faction, as a sort of huge, Mandalorian-esque group of mercenaries due to the fact society cannot forgive them and they're a bunch of clones - how much identity would they have without their leader? They'd be a bunch of outcasts, with no friends, unless of course The New Republic would extend a forgiving hand. Also, in the times of peace after the Empire - how would Stormtroopers, who LIVE for battle, even survive? I bet half of them would turn insane. Or maybe the ultimate fanboy wetdream could happen - Boba Fett takes lead of the Stromtrooper Renegades. All possibilities
You can also, like someone mentioned, play the Jedi Knight games - which have the theory that The Empire still functions, only not as strong and Emperorless, and is nicknamed "The Remnant", but, like my theory, it's basically a fan fic in the world of EU and means nothing really. Leave it up to your imagination. I quite like my Stormtrooper renegade faction/army. Sorta like the next generation of Mandalorians, with Boba Fett in control, carrying on Vader's work. Would be pretty cool.