Two to start with.

Two different bands:

1.  A synthesis of two bands.  Take the Talking Heads and the Black Crows.  Call it the "Talking Crows."  The music would be Black Crows songs with that straight ahead steady beat that the Talking Heads always use.  The vocals would be birds.  Maybe get some parrots, or just use bird songs, whatever.

2.  Ok, a band called "The Whom."  They would do acoustic covers of The Who songs.  Except all the lyrics would be edited to be completely grammatically correct and in full sentences.