You definitely need to take your dog to the vet, ASAP. Your dog is suffering and he needs to start treatment like yesterday.
There is absolutely NO safe home remedy for mange. Demodectic mange (non-contagious) nor Sarcoptic mange (highly contagious) can be distinguished without a skin test. Both are caused by mites that cause an infection on the skin which akin to being burned. Do not pour motor oil on your animal! This is an old country "remedy" that makes the infection worse and can easily be fatal. You need a bathing dip from your vet and antibiotics.
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