My '38 was the same way. My modern vehicles usually eventually get a layer of sticky yuck on them as well after a period of time. I suspect it's an accumulation of oils & dirt from hands building up. On my '38 I removed the wheel, filled a large pan with warm soapy water & used a bristle brush to clean it then painted it. So far so good. There are products on the market for cleaning hand gunk off of modern steering wheels.

Save a life, adopt a senior shelter pet.
The three main causes of blindness: Cataracts, Politics, Religion.
Name your dog Naked so you can walk Naked in the park.