IANAL, but I have heard that parody falls under Fair Use. For example, Weird Al Yankovic is an artist who has made a living by taking popular songs and putting new (and funny) lyrics to the tunes.
From what I’ve read, Yankovic is not required by law to get permission from the artists he parodies. He does so anyway, because he wants to maintain good relationships with the artists, but if were so inclined, he could parody a song with no copyright issues.
The Wolf