Helpful info on Smithsonian's website on preserving wood furniture that is applicable to a gunstock.
If you want to preserve whatever is underneath, start with the most benign method: water & a cloth & a toothbrush.
As you say, it may be the grime on the surface is soot from a wood fireplace, or ammonia from being stored in a barn, or years-ago attempt with linseed oil refinish, or wax. You may never get rid of the gunk on the stock, and there is a point where you should say "good enough." You may still see the cartouches, but imperfectly.
Abrasives, like steel wool, or chemicals like oven cleaner or paint stripper, will likely remove the gunk along with any original finish, leaving a stock that looks newly cleaned and distinctly not original.
