J.M.
He has a sinus infection, I can almost guarantee you. His nose doesn't have to be stuffy to have a sinus infection there are a ton of pockets and places for that mucus that is left over from his cold or flu to hide. When that yucky mucus sits in your sinus cavity it is PERFECT for bacteria to grow and just like bacteria in your mouth when you don't brush your teeth, it doesn't smell awesome. He is probably prone to sinus infections and if this is a chronic condition, he probably has some pitting where bacteria and mucus settles causing the bad breath over the years.
I highly recommend getting him to try a Neti Pot, it will help flush out the sinuses. I just got a good inexpensive one by Waterpik SinuSense (if you like them on Facebook I think you can get a coupon and it comes with the Saline solution). This WILL help the smell. I have a friend with the exact same problem. It should also help him regain his sense of taste within a week if he does it as frequently as recommended.