Like SFD, I immediately recognized the Back to the Future and Doom parodies. (What's that face in Devan's torso in the demo pic?) That Artist Formerly Known as Prince parody is a new one on me, though.
Frankly, the Episode 4 pic reminds me of Commander Keen 6, when that one-eyed alien was salting Keen's head. Probably not quite the best reference, but a general idea of sorts. But, the O in "Monkey" has the somewhat-trademark star in the middle, as does "Donkey" in "Donkey Kong."
What's with Commander Keen and his
obsession with being called Commander Keen, instead of Captain Keen (Keen 4)? Last time I checked, Captain was a higher rank than Commander. (That's why, when I mentioned to Firefox that I was going to promote him from Captain to Commander at the end of E:JF, he said that doesn't make sense, considering the preceding fact. Well, actually, he went into some long lecture about the ranks on Star Trek, and how Picard ranks higher than Riker, or whoever, blah, blah, something, something else. I wasn't really listening anyway. [Before anyone asks, I scrapped the idea soon after Firefox told me that. Don't expect anything of that sort at the end of E:JF. <_< {shifty eyes}]) Wouldn't it be better to be thought of as a higher rank than you actually are?
TSF is an illustration by Noogy. 'Nuff said. The good Dodrill thought the three Jackrabbits flying high above on their airboards -- especially Spaz, who doesn't look too confident of his balance...

-- would make a good cover pic, which is why it was used as both the box design (last I checked, anyway...) and the episode intro. Although, I don't understand what that diamond in Jazz's hand has to do with anything...
Now all we need to find out is where the parody came from for the Flashback episode pic, and then our heads will be even more full of useless knowledge than exactly twenty-four days, six hours, and forty-three seconds ago. Yay.
As for Jazz itself being a parody... *cough* Sonic *cough* (Not saying that Sonic is better than Jazz, of course. Jazz beats Sonic on all fronts. After all, I don't see Sonic toting a gun, do you?)
DoH is the end boss of Arkanoid ][. Anyone remember that game?