A tiny amount of stock oil, rubbed in with the palm of the hand, can be applied now and again – as long as it is allowed to dry thoroughly before the gun is next used.
However, too much oil will leave the stock sticky, which leaves it liable to attract all kinds of dust and muck, and also unpleasant to handle.
For regular maintenance, a good quality wax furniture polish is best. Just apply a little, being careful to keep it out of the chequering, and buff it with a soft cloth until you achieve a dull shine.
Some years ago my wife and I bought some European-made pine furniture, and in one of the drawers we found a tin of polish called Furu Wax, which was of Dutch origin.
It turned out to be ace for gun stocks, but I don’t seem able to buy any more.
However, I am assured that other good-quality furniture waxes are just as good.