If any of the Dust Bowl victims brought guitars with them to ease the difficult journey, it was likely bluegrass music that they sang around the fire. For a good introduction to the genre, check out the Smithsonian's compilations of classic American recordings.
Steinbeck was heavily influenced by the Mexican migrants he encountered in his work and travels. Norteño music provided the soundtrack for many Mexican-Americans along the border during the Dust Bowl and Great Depression.
Guthrie was raised in Depression-era Oklahoma and was forced to hitchhike his way to California when he was wiped out by the Dust Bowl, just like Steinbeck's Joads. The struggles of Steinbeck's characters had special significance for him. His "Dust Bowl Ballads" album, released in 1964, is a tribute to the era and to Steinbeck's fiction—the album features a two-part ballad entitled "Tom Joad."
One of the most famous songs of the Depression, this song was covered by countless musicians and was banned from some radio stations at the time for being too depressing. This version is by Tom Waits. If you're not used to Waits' voice, don't worry—he's not shouting at you.
If Steinbeck recorded the forgotten man's stories on the page, Bruce Springsteen recorded them in song. Springsteen actually received the Steinbeck Award from San Jose State University's Center for Steinbeck Studies in 1996. The award is given to an artist whose work reflects Steinbeck's empathy and belief in the dignity of the common man. Listen to "The Ghost of Tom Joad" and remember why the Boss rules.
The soundtrack to this 2000 Coen Brothers movie is evocative of Steinbeck's era—traditional bluegrass and folk music from the era of the Great Depression. It's a great compilation and pulls you into the period's sorrows and simple joys.