You can delete a song off of your phone by swiping to the left on the songs title. A red delete button will show up and then press the delete button. After this you'll see a cloud icon that you can push to redowload the songs.
Also, have you tried hard resetting your device?
Sometimes that helps free things up that get glitched. I don't have the paticular answer to your problem because I have not experienced it yet. I know sometimes things take a minute to start to play but that is with match turned on and it is having to dowload the file.
If you turn match off on your device it takes a minute to take everything that was not dowloaded off your device too.
If you turn match off on your device sometimes the best thing to do is plug it into itunes on your computer and resync it with your computer.