On a really foul 1868 Springfield I used half and half turpentine and linseed oil rubbed on by hand and stripped off with a coarse cloth. In the really bad spots I added just a bit of 0000 rottenstone and/or gently used bits of OOOO steel wool. It cleaned nicely without damaging the patina under all that grime. Your stock doesn't look bad at all and just linseed or lemon oil and a toothbrush should clean up the checkering.

Jerry Liles