Use of Wood Bleach (oxalic acid) after the finish is stripped is an excellent way to even up and lighten up the surface for staining and finishing.
It will open up the minut pores of the wood and allow a new stain to penetrate evenly and fully.
You can purchase it in crystal form in most home improvement stores in the paint & stain dept. Just mix with water. I use it warm,,mixed in a glass jar and placed into the microwave for 30 seconds or so. Keep the extra unused portion for the next job.

DO NOT use common laundry bleach. It will lighten the wood but will cause rust to the metal it touches in the future and most probably damage the wood.

If you use oven cleaner to remove oil/grease from wood (though many will cringe at the thought), follow it up with a bath in wood bleach to neutralize it afterwards. The oven cleaner is an alkali and the wood bleach an acid.
Plus the wood bleach will nicely lighten and even up the wood color for staining and finishing. No funky after colors that many associate with the ovencleaner treatment. Be very careful when handleing the wet wood as it is very much softened and will dent at the corners easily. When dry, it will be back to full strength.

The ovencleaner will only take the oil/grease off of the surface and that immediately below it. The deeply imbedded stuff will still be there and will slowly come back to the surface in time to push your new finish off if it isn't drawn off with something like the acetone or laquer thinner soak,,or the whiting powder applications.