I'm not sure exactly what the steering wheel is made of. It looks like bakelite to me, and, in view of when it was made, that's likely. Bakelite can be a bit fragile, so you want to make sure you clean it with something mild and non-alkaline.
If the problem is just built-up crud, plain ol' dishwashing detergent probably will do it. If you need to polish it, that might require a little more consideration. Best suggestion is to google "bakelite cleaner" or some such thing. Someone will be able to suggest a polish that will help. Whatever you try, test it on a small, inconspicuous area first.