So I found the link on "Streaming Music with Airplay" that seems to turn the Omega into and "AirPlay" device.
If I were to use this, then I would need a "player" that supports streaming multiple audio files to multiple AirPlay devices. On windows it looks like "Airfoil" by Rogue Moeba might do this. Also looks like they have a Linux package that can receive feeds called "Airfoil Speakers for Linux". The various free builds are at the bottom of the page.
I'm just wondering if I could really stream 12 to 20 feeds at once without issues. It might be better to find a player for each Omega and upload the different audio files to each Omega. Then my only challenge would be to have a way to check the status of each player to make sure they are still "playing."