Sixteen is quite a good age for your budgie, so it would seem that any injury or fall would have more effect on him than it would a younger budgie, especially since his reactions will not be as good. It sounds very much like your bird has damaged his inner ear, which is responsible for balancing.

This would make him hang his head to one side and will be disorientating for him. However, if his stools are softer than normal, there may be additional complications. I would recommend that you take your bird for a full examination.