The birch is fairly soft, and light colored. Don't be too agressive with physical/mechanical finish removal.
I've had good luck with hardware store paint removers. I prefer the gell over the liquid.
Remove the stock(s) from the gun. First, lightly scratch the finish, perhaps with a dinner fork, but not deep enough to gouge the wood. Just the exterior finish. Outdoors or in well ventilated area, apply the finish remover with a 000-steel wool pad. Let it sit for about 5min. Then, begin to scrape the old finish off with another steel wool pad, until youv'e removed all the old finish. Use a bronze bristle brush to remove finish from any checkering by brushing in the direction of the checkering. Some of the Glenfield/Marlins have etched/embossed decorations. Remove the finish from them gently with the bristle brush (the kind sold for gun cleaning/auto parts- not the big barbeque grill type). Then, wash off the remaining finish remover either with water or mineral spirits- however the directions on the remover label states.
Let the stock dry for a while (til dry, perhaps overnight). Lightly sand the exterior surfaces of the stocks. Be real careful not to sand much off the interior surfaces as this will affect the stock fit to the gun later if you remove any wood. Don't sand any checkering or decorations. Just use a small bronze brush to remove any residual stock finsh. Some even go so far as to mask the checkering with masking tape, or aluminum foil tape such as used to protect the plexiglass on aircraft being stripped and repainted.
I then after prepping the wood apply either a Minwax, Formby's, or Danish oil WALNUT stain. I prefer the dark walnut as it stains the birch a bit darker than the original finish. Don't worry, it won't come out black as it looks originally befor the excess stain is wiped off. If you want a more reddish hue like a circassion walnut, use a medium to dark maghony stain. I recommend if so, use a little of the mahagony mixed in with the walnut, as the birch is so light colored originally.
After staining, I then use either a satin or semi-gloss polyurethane varnish. I apply that either with fingers, or with a sponge-foam rubber paint brush. Don't try to put it on too thick, or you'll get runs. It will take 3-4 coats to get a good build up of finish, though I often quit after 2 for a rough duty gun. (ie: Remington 870's used for duck hunting.) realizing that in 3-5yrs I'll be doing another refinish.
After the finish is dryed (2-3days), if it's too shiny, use some 0000-steel wool to dull the finish.
Be sure not to sand too much, especially around the butt pad surface, or you'll have an usightly match between the stock and butt pad. Perhaps, even replace the butt pad before sanding and finish the stock with it in place.
Good luck with your project.