Have you tried different headsets in order to see if it is the headset connector causing the choppy sound? Also, try cleaning the headset jack with a wooden or plastic toothpick to keep the jack free from lint and grime.
Another thing that you can try is to reboot your phone in safe mode to see if the radio works better there. All apps downloaded from Play Store is temporarily deactivated while in safe mode, that way you can see if this behaviour is caused by a downloaded app or not. For more information on safe mode and how to use it, click here.