Last year I started a thread called Spike Jones/Homer & Jethro Songs and posted "Pal-Yat-Chee" there. (It's a parody of the opera "I Pagliacci") I was a bit disappointed that no one else posted any lyrics in it. I wish I had known about this thread!

These songs are in DT:
Daddy Played First Base (a parody of "Daddy Sang Bass")
How Much Is That Hound Dog in the Window? (parody of "How Much Is That Doggie in the Window?")
Li'l Ole Kiss Of Fire (The DT says it's a parody, but I don't know what of.)
I'm Movin' On No. 2 (parody of Hank Snow's hit)
So Long (It's Been Good to Know Yuh!) (a parody of Woody Guthrie's song)
The Battle Of Camp Kookamonga (parody of "The Battle of New Orleans")
The Billboard Song (3)
Winchester Cathedral (Parody)

The following songs are posted in threads:
Don't Jump Off the Roof, Dad
Flower of the Wildwood (parody of "Wildwood Flower.")
I Won't Go Hunting with You Jake
Mama Don't Whip Little Buford
Pore Ol' Koo-Liger (parody of "Kaw-liga")
Sink The Bismarck-No. 2 - parody of Johnny Horton's song.
Tennessee Waltz.

There may be more, but that's all the searching I have time for right now.