The API only supports a basic set of functionality, basic playback control with play, pause, playpause, previous track, and next track methods, and the ability to access name, artist, album, duration, artwork and rdio url of the current track.
For example from the command-line you can type:
osascript -e 'tell app "Rdio" to play'
and that the desktop app will begin playing. You can also ask the desktop app to start playing a specific track, playlist or album:
osascript -e 'tell app "Rdio" to play source "t2910908"'
Or to get the name of the currently playing track:
osascript -e 'tell app "Rdio" to get the name of the current track'
You can use Automator or the AppleScript Editor to build more complex integrations.