How to stop my service?

Question

Please also see Edit 2 (below)

I have extended NotificationListenerService and implemented several of its methods including the onDestroy()

Answer 1

Try overrides onStartCommand() in your Service with START_NOT_STICKY flag:

@Override
public int onStartCommand(Intent intent, int flags, int startId) {
    super.onStartCommand(intent, flags, startId);
    return START_NOT_STICKY;
}