You might have a broken axle inside your rear hub.

Remove the wheel from the frame and it should be fairly apparent if this is the cause. If broken the axle should come out if you have a bolt-on hub, if you have a quick release hub then it should come out after removing the skewer.

If this is the case then the bearing surfaces inside the hub could be thrashed...you will need to inspect them to see if you can get away with a new axle or if you need a new hub altogether.

-j