Walter Snyder's answer is probably closest to being correct. An extremely dry piece of wood didn't lose linseed oil, walnut oil, or lemon oil. It lost an excess of bound water from its' cells, and once it has reached that point, adding oils or finishes will only inhibit the return of moisture. If you bring extremely dehydrated wood to a more humid climate, lost moisture will slowly return, but stress drying cracks will not magically heal themselves. And oils will only make it more difficult to stabilize and fill these cracks. Equilibrium moisture content in most of the U.S. is about 12%, and kiln dried wood used for furniture is typically dried to around 6-8% which keeps it pretty stable with the indoor humidity of most homes.
Once your "dry as a popcorn fart" piece of wood has reabsorbed as much moisture as it will in your climate, which may take months, you might be able to stabilize the stress cracks with filler coats of thinned clear epoxy, and then doing the final filling with a slurry of thicker epoxy and fine sanding dust. If this is gun stock wood that is already even with or slightly below metal surfaces, you would want to absolutely minimize any sanding of the stock surface, so you could use very fine walnut dust from another piece of walnut. I'd use a vibrating electric sander or random orbit sander to make my pile of very fine sawdust. Of course, walnut sawdust mixed with epoxy gets pretty dark, so you might wish to use lighter sapwood dust. Using the plastic spreaders used for auto body filler might make it easier to do this filling without excess build up on the wood surface. And you'd want to use a slow setting clear epoxy to give yourself time to work before it starts setting.
