Welcome to YorkieTalk.
Losing teeth like that is a very serious issue. With only three teeth left not much can be done now, however, if the dog is well enough to go under anesthesia it might have to have something done with its gums. I am guessing that it is periodontal disease. My Yorkie has stage 3-4 periodontal disease (4 is worst). A couple of her teeth fell out almost a year ago and she had to have surgery to get about 9 pulled. The rest of her teeth seem to be fine now. There was no choice in pulling them since leaving an infection in the mouth can lead to disease of the organs. I would definately get another opinion on the teeth. I think you will have to go with all soft food now. In that case find his favorite (or make it yourself). Getting that skinny that fast isn't right and I would take him to a vet. In the meantime have you tried things like pasta to try and fatten him up?