I clean my oil finished wood stocks with a oil scrub.

I cut raw linseed oil with turpentine to a 20%/80% mixture, then scrub the wood with a very fine scotch-brite pad.  Remember, you are trying to lift the dirt and grime out of the grain, while not removing any wood in the process. 

Work in small sections at a time, then wipe the oil and lifted grime with a clean cloth.

Once you are finished, wipe the stock down again with a cloth moistened with turpentine, allow the stock to dry for a day or two, then repeat.

When the stock is as clean as you want it, rub in a few coats of linseed oil.

Original 1903 stock after an oil scrub.  After cleaning it up, the handling marks from the individual that it was issued to became visible. :)

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