I had a smelly cat rescued from a kitty mill. She had funky skin and fur and smelled funny for months. But with care, she healed up and smelled just fine.
Don't forget, these poor pets are seriously traumatized from these experiences and like humans who have survived trauma, take a few months to even years to recover. A good vet will help you to find the source of problems and get him on the right track to health.
Smells and health on a pet go hand in hand. Rest assured, he will smell better as he recovers. Their skin, fur, waste and smells will improve greatly from a top notch diet. I know they're pricey, but pet foods like Eukanuba or Science Diet are formulated to help pets digest food more effectively and are fortified with nutrients etc that will help improve their coats and skin.
Avoid using perfume (even pet products) insecticides (flea collars and powders) and fancy pet shampoos. The vet is right. Oatmeal wash is the way to go until his skin heals up. Otherwise you risk prolonging and worsening the condition.
Make sure he has a soft bed. This will help him heal up too. The more expensive ones have natural smell repellants (like cedar) in them to control the doggie odors.
Be sure to brush his teeth with a dog toothbrush and paste...or pay a groomer to do it. Bad teeth and tartar can make an entire dog smell mighty bad. No need to do this everyday like for people...but at least once a month and give him teeth cleaning bones in between to keep him smelling good and his teeth clean.
Don't leave him outside. Dogs love to roll in smelly things. If he's in more than out, less chance of him doing those doggie things, and that means less chance of him smelling funny.
Sometimes castor oil on a cotton ball dabbed on dry or sore patches can help speed up healing. Do not over do it, as castor oil can cause loose bowels if he ingests too much. So dabbing is the way to go...enough to soften and soothe the patches, not enough to get things going if he licks himself. Soaking in Epsom Salt is helpful too.
Any chance the doc gave you any sort of antifungal or antibiotic to help speed healing?
I agree with others who've suggested cleaning the ears. That's another spot that can get smelling if there's infection. The doc should have noticed and given you a cone and antibiotics if that's the case.
I know he's bugging you now...but mark my words. The little "stinker" will grow on you. And he's going to love you to pieces for saving him from the shelter. Dogs are incredibly loyal and loving if you give them a chance.
I promise, when he gets healthy, he'll smell just fine. Dogs generally do not stink if they're not neglected or sickly. I have big labs and people are always shocked when they find out...saying by looking and smelling your house I"d never known you had big dogs.
If you keep them brushed and cared for, they'll be clean and pleasant companions.