I have made some very funny comedy songs in my day, and I actually am on here for the sole purpose of seeing if any of you guys want to make AMV's for my music. So if you are interested, here's two you might find funny, one is called "The Ballad of John Bob Bill", and another is "The Greatest Song". Another one that's not super funny but could make a cool/funny video is called "Dance Like a Monkey". I don't know if they will be what you are looking for, since you may be wanting more of your creativity to make the comedy, and less of the song itself, or you may want to use a song people know, but I'd at least listen. These songs could easily become memorable to the public as they're very catchy. Here's the urls if you're interested.
http://soundclick.com/share?songid=7106876
http://soundclick.com/share?songid=7105329
http://soundclick.com/share?songid=7106856
Come to think of it, I bet you could make something really funny with "Dance Like a Monkey". But if you don't want to go with any of those, have you thought about The Talking Head's "Pull Me Up" (I think that's the name) or Adam Ant's "Goody Two Shoes"? There's also Cibbo Matto's "Birthday Cake" and "Chili Down" From David Bowie's Labyrinth soundtrack. Oh, and don't forget the Muppets "Manumanuh".