It's not hard to strip paint. I would use paint stripper (the ones wit methylene chloride are still my favoiretes but all of this stuff has health hazards associated with it. There is NO respirator that can filter out methylene chloride for more than a very short time. You work outside, and keep the paint stripper downwind.) They I'd use 50/50 denatured alcohol + lacquer thinner and 000 steel wool and perhaps some kind of brushes, wire or otherwise, to clean out the last of the paint. They I'd wipe off any residues, let it dry, then steel wool with the 000 again. Then apply wood stain as needed or to desired color. They shellac over it with either clear or amber shellac. Amber over oak gives pretty ,uch the original color, I am guessing.
The problem with paint on oak is that oak has big open hollows in the grain and paint will go in there and you'll have top clean out the grain. (Why I said a brush.) The plus side of this is you have shellac on the machine with paint over top, most likely. And shellac has no chemical resistance whatsoever, so most of that paint will pop right off there when the shellac lets go. But depending where you are, you might be into fall weather and spring and summer are better times to refinish furniture if you are working outdoors or in unheated / un-dehumidified shop or garage.