Yes to the wash and oil, you may want to think about zinc deficiency? Although if you feed Caprivite it shouldn't be an issue.
I have a male with very scabby skin (and was treated for mites with Panomec, 3 injections 1 week apart each). I have also just given him a mineral drench, and bought him a Zinc rich Rockie - just need to work out how to fasten it in his pen somehow...