My dog has a really bad rash.

[Paddington]

Well my dog Paddington is about 3 human years old now and he has a rash that has been getting progressively worse for some time now. His skin has gotten discolored and the rash flakes pretty badly, the smell is awful to boot, he spends a lot of time licking it which makes him slimy most of the time. He doesn't seem unhappy, he's just very clearly diseased. He's had a history of busting into places he doesn't belong and eating some pretty terrible things, a lot of over the counter medicine and soap for some reason. I'd say its a miracle he's still alive with some of the things he's done. My family really loves him but he's getting hard to live with because of his destructive tendencies and the smell and flakes that seem to get everywhere and be on everything. He's seen the Veterinarian who is pretty much stumped at how he's still alive and says the condition may be due to his dangerous eating habits. We really don't know what's wrong with the poor little guy, and suggestions would be really appreciated.