On Edison it should be pretty much the same in terms of commands. For software installs you can use my repo and the apt-get equivalent here is opkg.
I don't have such a soundcard at hand, so can't help you step-by step, however in general that would be:
- Install the snd-usb-audio module, alsa utils and mpg123 with "opkg install kernel-module-snd-usb-audio alsa-utils mpg123"
- Plug the soundcard, try the alsamixer to make sure it recognizes the device
- Run the mpg123 with respective arguments to play what you need. I haven't used mpg123 so don't have these at hand.