Go to Wally World & buy OOOO steel wool, a can of Homer Formby's Furniture Stripper, a small can of Min-Wax stain/finish/sealer in the tint of your choice (red mahogany is a nice color for Winchesters)- and a small bottle of Tru-Oil stock finish at a gun-shop if WW doesn't have it.
Follow the Formby's directions to strip your stock(s) with Formby's on a pad of OOOO steel wool, let dry overnite then stain/seal them with the Min-Wax.
The next night start oiling your stock by dabbing one fingertip into the Tru-oil, and start working that one drop into the wood until it's about the size of a dollar bill, and it's just about tacky- your skin will start to "squeak" as you rub.
Immediately that area is done, get another drop on the fingertip and start in on an adjacent area, doing the same procedure as the first area.
Repeat until the stock is covered with one coat and hang it up to dry overnite.
After the 2nd coat dries overnight, rub the stock with the OOOO steel wool until the visible finish is gone. Clean all steel dust off the stock with a magnet and a clean cloth then start in applying the 3rd finish coat.
Depending upon the stock wood and your tastes, the stock can take anywhere between 4 and 6 coats, rubbing down between each coat after the 2nd coat.
If you like a shinier finish, leave the last coat untouched, except for an application of a good automotive paste wax. Don't use polish - polish is an abrasive.
If you prefer a more satin finsh, lightly rub the last coat with the steel wool, use the magnet, and wax the stock.
Don't forget to apply one or two coats of oil inside the inletting, on the unfinished wood & under the buttplate (no staining, rubbing, anywhere there).
If you let the finish dry overnight between coats, you will get a better, more durable finish than if you hurry the job. It'll take about 30 days for the finish to fully "cure", so try to keep cleaning fluids, etc, off it for awhile. (the wax will help)