As far as unusual goes...
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Here are some good example of songs that I've never ever seen on TV:
Joanna Newsom - Sprout and the Bean
Beirut - Elephant Gun
Devendra Banhart - Feel Just Like a Child
Don't Turn Away (The YMCA Sportspark Anti-Massacre) by The Lost Trailers.
Anything by The Fiery Funaces.
"My Dog Was Lost But Now He's Found"
"Tropical Iceland"
Also can't go wrong with everyone's favorite superhero band, The Aquabats.
Fashion Zombies!"
"Martian Girl!"
I would have to hit the musical way-back machine and go with Razor - Evil Invaders. I don't know if it got any MTV airplay at all back in the day (except the obvious Headbangers Ball, and even then, thrash bands had trouble getting their stuff played on there)
And just now, I discovered this band from the UK called Evile. I discovered them through the fact that they are touring with one of my favorite bands. This song is the title track to their debut album, "Enter The Grave" (which was released about a few months ago).