Severe Itching to the point of bleeding

[Q222]

My dog has a severe itching problem. It has gotten so bad that she has to wear a e-collar all day and all night now. If we take the collar off she immediately starts chewing her feet and her rear. She makes herself bloody and sore. She then limps around for 2 days. If I let her she would chew herself for hours straight. She had allergy tests and we took out the allergens from her diet. All of them. She is not getting any better. We took her to the vet and they have tried benedryl and prednisone. None has worked or even helped. I don't think it is D or S mange mite. She doesn't have hair loss. She is VERY greasy and smelly. She has a thick layer of oil on her. Even 1 day after a bath it comes right back. I have never smelled a dog that bad. With her greasy skin and constant chewing what could this be besides regular allergy's because I know it is not just that? Thanks for your time!!!