Can I use my own music instead of the in game radio stations?

Yes you can, you'll need to mod your game. Here's a good walk-through for doing that including the tools you'll need.

Basically, you'll need to:

1. Modify files in steamapps/common/saints row the third/packfiles/pc/cache
2. Extract the audio files from the radio_*_media.bnk_pc files (or a specific station you want)
3. Transcode your audio files to vorbis (the link gives you details of the encoding options you need), they'll have the .ogg extension.
4. Change the metadata for the bnk_pc file so that they point to your new songs (there's 2 files you need to change)
5. Repack the radio station files using PackVPP and copy it into steamapps/common/saints row the third/packfiles/pc/cache