Theoben used custom stocks stocks on their guns and I was told they were varnished not oiled. Not sure if that true.
If it is then I doubt oiling will make ant difference.
Just been on their site and found this .
Although Machinery is used for the initial shaping and in-letting of the rifle stocks manufactured, each stock is finally finished by hand, which includes sanding, staining, lacquering or oiling. Great care is taken during the sanding and finishing of all our air rifle stocks to achieve a high quality consistent finish to a semi Matt sheen that is both aesthetically pleasing and hard wearing in most conditions.
Possibly theoben specified lacquer as they were beech stocks on most unless it was walnut fitted.