If the extra length of the forend beyond your 36" bbl is oil soaked, cut it off now and get it away from the rest of your project.
It can only make for more problems as you transfer oil to other areas of the wood. Plus it can begin to migrate on it's own back towards the breech deeper in the wood.
Leave a small amount excess for working (1/4" or so), but the rest of the oil soaked wood can go.
Any part of the remaining forend that still has the oil in it,,take some time to draw it back out. It'll do nothing but spoil any wood finish you try to apply,,especially staining.
Any fine grained powder material that'll absorb the oil as it is drawn to the surface will work. It isn't a fast process, but at least your's hasn't sat for a century or more saturated with wheel grease.
Stock makers and wood workers often use 'whiting powder'. I use it alot. I think is calcium carbonate powder.
But I've used things like kitty litter,,or other commercial dry powder products sold to absorb liquid.
Stuff the end of the stock in a container of the material for awhile. Check, brush off the adhered oil/absorbant material and place back in till no more oil is draw out.
Like I said,,it isn't fast but it works.