If the vomiting and the running around started about the same time, they may be related. He may have a sudden attack of nausea or internal pain when he is sleeping.
If he were mine, I would start by trying to find the reason for the vomiting, but there are dozens or reasons that cats vomit.
You could start with something simple like giving him 1/4th of a 10 mg Pepcid AC or famotidine at bedtime. That might suppress stomach acid, nausea and vomiting, and see if he sleeps more normally. If he does, then the problem is the vomiting, and the treatment might be diet change, testing for inflammatory bowel disease, checking for liver or kidney
or heart problems.
If the Pepcid seems to make no difference, then the nighttime running may be unrelated to his vomiting. You could try giving him 1/2 of a baby aspirin twice weekly for arthritis pain and see if that helps. No other over the counter medication is safe in cats, tylenol is especially poisonous to cats. If you try it, do not give more than 1/2 baby aspirin twice a week.
Let me know what else I can help with or answer. Rebecca