First thing you want to do to get rid of the grease is to remove all the metal from the wood so you don't have to worry about the metal. I get a big ziplock baggie and put all the small pieces in there.

As for the wood, depends if it's wood or laminated wood. Laminates you want to be less aggressive with as they can separate. My favorite for getting cosmolineicon out is to put the stock on the dashboard of my truck, with plenty of papers underneath it and the window facing the sun. It's a gentle heat but plenty hot to get the grease to pour out of it. 3 or 4 days of that and it's pretty dry. I then spray it with a spot remover or grease remover, K2R is my favorite for this.

Other methods that work for those in more of a hurry are oven cleaners. Some guys put the wood in their ovens if they fit. I don't recommend this one as you can too easily char the wood. What I did with my Mosin Nagants is I built a small enclosed cardboard box that the stock would fit completely in. I then put the box on top of a pair of portable radiators and left the heat draw it out. Didn't work quite as nice as the dashboard but in the winter, you do what you have to do. Don't leave them unattended, probably a bit of a fire hazard.