Hello. You need to take him to a vet.
But, there's some good news here.
Even if you can't afford the fancy tests, at least get in for the evaluation, to ensure there is not a more serious condition.
Many vets are now offering new clients a free examination. So call around.
Lots of vets where you live. I'll bet you can find that free exam.
Then, at least they can direct you based on the smell and condition of the skin what type of products you may need.
Yeast infections can smell like that, so you may be wasting your money with all those shampoos, etc...
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This odor you are describing can be an indication of a yeast infection, an oral cavity problem, and even kidney disease can cause the breath to smell like sulfur. The coat continues to smell because if they groom themselves the odor goes all over the body. I can't say with any certainty what you are smelling is even a serious problem or not, but you need that free examination to at least start there.