Kerryman:
Cheap walnut definitely can be improved with an oil finish. What you are dealing with is probably open-grained black walnut similar to that used on U.S. military rifles as well as inexpensive sporting rifles and shotguns in the 50s and 60s which would now be stocked in birch. An oil finish often brings out more figure than you would suspect. Consider linseed for the first coat to darken the wood slightly and make it "glow", followed with tru-oil or similar (or a mix of tru and BLO to soften the look), or wet sand as you were thinking. I think these look nice with just a few thin coats of tru-oil, not totally filling the grain. This avoids the "plastic" look that modified oil finishes seem to get when built up too perfectly.