Hi! Sorry to hear about your pup's odor problem, I think you may be on the right track about food being a problem.
I had a wonderful setter once, she developed an odor problem too, and had substantial hair loss, as well as problems with the wax in her ears. Had her to several vets, but no one was ever able to pinpoint the problem exactly. After much trial and error, discovered she had a food allergy, even tho she was on some popular and well-recommended chow.
Went to an all natural food with none of the bad preservatives, ordered the stuff online as I could not get it here, and gave her lots of baths and soothing skin treatments, and she recovered about 95%. Also was super sensitive if a flea disregarded her flea coller and bit her.
Your pup may have allergies, but once you figure out what it is that is bugging her, you'll both be happier!
There is a lot more food to pick from now, if you want I can let you know the name of some good food I have used for my four footed buddies.