How many times per day does he vomit?
How many times per day does he have diarrhea?
What is his normal food?
What does he eat for treats?
Now that I am thinking of it, he has been lying around more than usual but I guess that would be the case if you were experiencing his symptoms. He also seems a bit thin to me. Very bony feeling when I pet him.
I would be most suspicious that he may have a case of pancreatitis. Your vet can check for this with a quick blood test. The primary symptoms of this are vomiting, diarrhea, and poor appetite. With his age, other possibilties exist, too, and I would definitely get him in to your vet for a pancreatitis test and exam. If it is pancreatitis, he will need hospitalization for a couple days and IV fluids to resolve the problem.
Let me know if you have more questions,