I'm no expert, but it does look like silky oak. It is very art deco in style with the drawers. Great find!
It could be silky oak veneer on the front of the drawers as some of the other wood does not look like silky oak to me. It's also pretty hard to tell from the photos. Good luck.
I've spoken to the curator at work who knows quite a bit about furniture history, and he's of the opinion that it's a pine table with silky oak drawers, dating between the 1930s and 1950s (due to the Queen Anne-style legs). So I'm going back to the plan of stripping and painting (except for those drawers!).