With Icecast you can run your own internet radio stream from an onion address. As always, be careful about copyright issues and preferably stick to Creative Commons music or music files that you own.
This system isn't intended to broadcast to large audiences and the upper limit of listeners is set at ten. So a family and friends type group.
Icecast is quite CPU intensive. For example on an A20 based system it takes about 70% of the CPU resource. This is something to be aware of if you're running multiple apps
1. Add mp3 or ogg files to a USB drive
2. Plug the USB drive into your server, then go to the Icecast app settings, add some details about your playlist, and select 'Update'
3. In a Tor browser navigate to the onion address for Icecast and you can then play the stream
It's possible to add jingles which will be played between tracks at random intervals. If some of the audio files on your USB drive are named jingle_something.mp3 then they will be used as jingles