Image via Vintage Lulu, found in Flappers & the Jazz Era photo pool.

Jazz Era music is so fun. A little goes a long way (some songs were only meant for dog's ears), but when it's good, it's really good--and the lyrics can be v. amusing (e.g. "You Gonna Look Like a Monkey When You Get Old"). Four online sources for Jazz Age swing:

1. One good bet is the WFUV's The Big Broadcast, a weekly radio show featuring music from the '20s & '30s. Hosted by Rich Conaty, the show plays every Sunday from 8 pm to midnight; the last two broadcasts are available online as streaming audio. Conaty also has a nice set of web recommendations (via getTRIO).
2. One commenter recommended the similar WAMU 88.5's Hot Jazz Saturday Night, which features jazz from the 1920s through '40s.
3. Fans of Bertie Wooster's singing will appreciate this set of links. Unfortunately, the official Jeeves & Wooster soundtrack has been removed, but you can still catch some of the songs on YouTube (e.g. "47 Ginger Headed Sailors").
4. Metafilter also has a good set of pre-1950s music links.

Finally, here's a YouTube clip of Josephine Baker's "Don't Touch Me Tomatoes." It's not quite the right decade, but I love her voice and the silly lyrics: