Okay, despite my title, it's only one song,.
But Joey Ramone did record a tune called "The Wonderful Widow of Eighteen Springs" with the text adapted from Finnegans Wake and the music written by composer John Cage. The excellent Open Culture website has a blog post that allows you to listen to the song. As Josh Jones notes, "Ramone’s interpretation of the piece is enthralling simply as a piece of recorded music. But it’s also a fascinating piece of cultural history, representing a confluence of the foremost figures in early twentieth century modernist literature, mid-century avant-garde music, and late century punk rock."
The song is from a "various artists" album, Cage/Uncaged — A Rock/Experimental Homage to John Cage, available on Ubuweb.
Hat tip, John Merritt.
For a choral piece based on a text from Finnegans Wake, by composer Robert Erickson, go here.