There will always be a big debate on this issue, but I will chime in.
First, be sure the stock is separated from the receiver and barrel -- this may seem obvious, but some forget.
Second, I have watched videos where "authorities" butchered guns with oven cleaner in a tub of hot water and a wire brush. OWCH, that's Bubba the Butcher.
Third, I try to stay away from hot water, as it can warp the wood. Same with putting a stock in the sun, even in a plastic bag; or putting a stock in an oven -- these can result in a warped stock. (You might get away with it, but sun/heat warps stocks, especially when heated unevenly).
Fourth, diagnose the oil issue -- is it just crummy old linseed oil, or is it a cosmolineicon soaked stock? If it's just old linseed oil, rubbing alcohol and fine steel wool is probably enough to get the surface junk off. Varnish remover can be used if it's varnish. Denatured alcohol if it's shellac. Then you can soak overnight in turpentine or mineral spirits and then wrap in paper towels or rags or embed in saw dust, changing the "diapers" regularly to keep absorbing. (I've even seen people put it in cat litter).
Fifth, if it's cosmoline, use the turpentine or mineral spirits and fine steel wool then the "diaper" treatment.
Once the junk oil is gone, treat with BLOicon until it absorbs no more, rub hard with an old towel to polymerize the surface with hand-rubbed heat, then (and the purists will cringe) finish with tung oil. (Why? because BLOicon will turn brown over the next 10-20 years, and after 50 years will be chocolate brown; tung oil keeps the BLO from oxidizing, is a better fungicide, and repels water better.)
Just my opinion -- others may not concur -- but it has worked for me.