DO NOT USE OVEN CLEANER!!!!!!.
Oven cleaner is a lye based product (Sodium hydroxide) Sodium hydroxide is about as powerful a base as you can find (PH of 14). Yes the solution is dilute, but it's still enough to cause chemical burns to skin in seconds leaving that skin sensitive to light for weeks afterward. Lye is a primary ingredient in the solutions paper mills use to dissolve wood chips into pulp. Is this something you want to put in contact with a 60 year old wood stock? HELL NO.
What Lye does is it eats into the lignin that bonds the wood fibers together, this will leave the surface wood punky and weak, potentially destroying the proper fit of wood to metal required for accuracy.
Lye is also a a chemical dye, well, not really a dye so much as a colorant. It will generally darken wood, but can also cause it to radically change color. In some cases it will react quite dramatically with contaminants in the wood, prior stains, oils, etc. to blacken the wood or turn it green. Lighter woods especially tend to take on a green hue after being exposed to oven cleaner and lye-based strippers.
Some time ago, sodium hydroxide and potassium hydroxide were both staple ingredients for commercial stripping operations simply because the stuff would eat just about any finish in short order. The problem was that it also ate the glues that held the furniture together, made the wood punky and discolored and ruined it's ability to take a finish well. Many lawsuits later, they all but abandoned lye as a furniture stripper except for the most stubborn finishes. Instead they work with safer and more controllable Methylene Chloride strippers. These strippers are more safely handled, less damaging to the wood, nearly as effective and can be more easily cleaned off of the wood without requiring neutralization. You can buy them at any hardware store under any of a dozen or more names including Zip Strip, Strip Eeze, Dad's, etc.
I classify Easy Off and similar "stripping solutions" as false shortcuts and lazy man's mistakes. Stay away from them.
BTW, I'm not just repeating something someone else has said. I used a lye-based stripper on a number of different projects and while it did cut through the nastiest of built up paint and varnish finishes, it also severely damaged the wood (lots of it) requiring extensive repairs and replacement. The companies that manufacture lye based paint and varnish strippers do not recommend them for woods that will receive a clear finish. Why? Because the lye generally discolors the wood.
Your mileage may vary, but the fact that none of the top three furniture refinishers in the business (Jewitt, Dresdner and Flexner) recommend lye-based chemicals as strippers except in the most extreme cases), should tell you something. Ignore their advice at your peril.