Is there any straight-forward way to make an Android app that streams an online radio station? This radio station will be built by my company, so there exists no API or anything at the moment. Ideally I am looking to make an Android service so that users can listen to the radio while the application is running in the background. Thanks!
The question you asked leads to a broad answer. However here goes some tips for you.
For a streaming radio station you can create a steaming server or buy streaming hosting. There are some free software's available that can be installed in your server and use to produce audio streaming from tracks/audio input.
For free streaming software you can try,
http://www.shoutcast.com/BroadcastNow
If you want to buy a streaming hosting service with pre-installed software like SHOUTcast try this,
Once you buy or host a radio station, you can connect to that station using a http://ip_address:port_number using Android MediaPlayer.