Although their name might not mean anything to you, you've probably seen the Brett Domino Trio's version of "Bad Romance" by now (and you really ought to see the Timberlake Medley). Now, I'm not really sure if they actually are a satire band.
If you're familiar with the Flying Lizards and either their album "Top Ten" or their single for their cover of "Money (that's what I want)", you know how they're pretty much known for doing well-known songs in a monotone singing style and minimalist electronic instrumentation. If you're familiar with the Residents and their album "Third Reich & Roll", you know how that album is mostly comprised of two huge medleys of classic rock songs, albeit done in a way you might hear if you were having a nightmare about the song. I could really call either of those "satire", since that makes it sound like the whole point is the jokiness of them.