My cat smells really bad?

I have an 8 year old cat with a flea allergy. She smells REALLY bad, sorta like greasy hair, moldy cheese and damp. I asked a vet about what I could do, but the vet just said "She doesn't smell." as soon as the question left my mouth, without sniffing her or anything. I know all cats smell a little odd, but I've never had a cat like this before, and I've had a lot. Ugh. Anyway, she gets really dirty sometimes so I have to wash her back or her paws and the smell goes away for a little while in those areas. I figured maybe the smell is because of her allergy? If she isn't given flea treatments and occasional injections, she scratches herself enough to bleed and licks her fur off. Is there anything I can do? Can I get her to be ok with having a bath with pet shampoo? Or maybe some kind of febreeze or SOMETHING? It's really gross.