Here ya go, list of all songs and the artists that made them.
■Mighty, Mighty Man by Roy Brown
■Let's Go Sunning by Jack Shaindlin
■Anything Goes by Cole Porter
■I Don't Want to Set the World on Fire by The Ink Spots
■Way Back Home by Bob Crosby & The Bobcats
■Butcher Pete (Part 1) by Roy Brown
■A Wonderful Guy by Tex Beneke
■Crazy He Calls Me by Billie Holiday
■Civilization by Danny Kaye with the Andrews Sisters
■Easy Living by Billie Holiday
■Happy Times by Bob Crosby & The Bobcats
■Into Each Life Some Rain Must Fall by The Ink Spots featuring Ella Fitzgerald
■Maybe by The Ink Spots
■I'm Tickled Pink by Jack Shaindlin
■Boogie Man by Sid Phillips
■Jolly Days by Gerhard Trede
■Fox Boogie by Gerhard Trede
■Swing Doors by Allan Gray
■Rhythm For You by Eddy Christiani
If you like their songs featured in Fallout 3 I would suggest looking more into each of these artist's music.
Some of the songs listed are from before the 1950s, I believe the Ink spots in particular were popular during the 1930s.
still on the same note wouldnt their been more songs in the fallout Universe such as Jazz,Classical or even country
Fallout New Vegas has them (country, classical).