They are mostly comprised of bikers and people from work release programs in prisons.
They love the music of the Rolling Stones.
The Fun Gestapo was first set to guard Val Kilmer's Family Thanksgiving Showdown so that people wouldn't miss the Price Time. They worked together with the Outcasts (not the videogame) on this assignment and it was considered a grand success.
The Fun Gestapo made a brief reappearance in Potoid 234. After Jim fails to negotiate with a crackhead (played by Holmes), the TFG arrive to "tazer him, drag him out, and leave him in a fucking dumpster where he belongs".
The Fun Gestapo comes equipped with tazers, prods & 3 gram bags of crack cocaine, that they are free to use on anyone they wish.