finishing a old gun shock?

Looks sanded and three or four coats of Tru-Oil hand rubbed in.

rc

Start by dampening all the dings with water to raise the dents & dings.
Using a wood burning tool, or soldering iron ...( test on cardboard ..for right heat)
fry off each water puddle. If the heat tool is way hot... place a soaked patch , on top off the dent. (trial & error)... the dents & dings will raise considerably

For raising dents, I use a damp wash cloth and a garage sale iron, set on the highest setting.

+1

A Wet rag and the wife's clothes iron is all I've used for 50 years.

Works amazingly well unless the dent has cut through wood fibers and steam pressure can't pop them back out.

rc

"...of Tru-Oil..." Or real pure tung oil. Absolutely has to be rubbed in properly over several days.
A great deal depends on the kind of wood your Stevens has. Some low end woods like birch have little or no grain and won't ever be exactly pretty. Mind you, tung oil will still give a dull stock a nice sheen.