Hi, Linda - I don't know about the legalities of parodies in general. However, I do know a bit about "God Bless America." Click here for information. Now, since the song was written in 1918, you would think that the copyright would have expired (songs from 1923 and earlier are generally in public domain - later songs will have to wait longer, thanks to Sonny Bono). However, Irving Berlin withheld the song until Kate Smith recorded it in 1938. That may make 1938 the copyright date (you'll note a 1938 copyright on the sheet music at the site I linked to).
Irving Berlin assigned the royalties for the song to the Boy Scouts and Girl Scouts of America.
The Irving Berlin people seem to be even more strict than the Rodgers & Hammerstein organization about protecting copyrights. You'll rarely find Irving Berlin songs in fakebooks, and I understand that's because it's so difficult to get the rights.
-Joe Offer-