Once you sand to 1000 grit, #0000 steel wool is grinding it back to about 220 grit, which you probably need to do anyhow, because 1000 grit burnishes the pores of the wood closed so that finishes are NOT going to adhere well.
Anything over about 320 grit should be reserved for polishing the finish rather than the wood.
Start at 80 grit and get the wood smoth (get rid of the divots and gouges. Then go to 120 grit, then 150, then 180, then 220 grit. At 220 grit you need to evaluate once and for all what sort of finish you will be applying to the grips to protect the wood. You don't need to go any higher than 220 if you will be applying polyurethane, varnish, lacquer or tru-oil type polymerized or oxidized oils. If you intend to finish with boiled linseed oil or pure tung oil, you can go up to about 320 or 400 grit without significantly affecting oil effectiveness.
If you are planning on going with BLO for a more natural sheen, then go from 220 to 320, sponge the wood (dampen it to raise the grain, then sand smooth with 400 grit paper, Don't overdo this though or you will cut away the grain that you just raised and the grain beneath which was not affected, will cause trouble down the line.
At 400 grit you can begin applying oil. The first coat can either be thinned with turpentine or mineral spirits or heated over a hot plate. DO NOT heat thinned oil. Wet the wood thoroughly and keep it wet for 30 minutes or so. Then dry all the excess oil off the wood as completely as possible and leave the piece alone for 24-72 hours depending upon the specific oil and weather conditions. Check back periodically to wipe up any oil that seeps back out, but don't get anal about it yet.
Buff sand lightly between coats with 600 grit paper. This will get rid of any oil that may have surface dried to a tacky feel and will give the next coat a good base to penetrate into the wood. wipe away the residue with a mineral spirits dampened cloth and allow that to dry for a bit before doing the next coat.
After the first coat you can "Stretch" additional coats onto the wood. Stretching oils involves applying a miniscule amount of oil and spreading it out as thinly as possible by rubbing it. For a pistol grip we are talking about dipping the very tip of a q-tip into the oil, dotting it onto the gunstock and then spreading that out. When it gets dry and you feel no more oil, dot the q-tip down again and so on. Absolute minimum oil should be applied so that there is almost no excess to wipe off when you are done. (But wipe it off anyhow.)
allow 24 - 72 hours to cure depending upon weather conditions. Hot dry conditions will allow faster cure time than humid and or cold conditions.
This is going to take a while though.
Pen spinners used varnishes to finish their products and they apply them on the lathe so they get maximum friction and heat to speed curing and to burnish the wood and finish in.
If you want a similar degree of polish, you might want to go with Tru-Oil or a similar film building finish or varnish. You can stretch Tru-Oil on or just bathe it on, let it dry and then sand off the excess before applying the next coat. Same is true of varnishes and polyurethanes. You can also thin varnishes and polyurethane with Mineral spirits to produce a wiping varnish. 2 to 1 ratios favoring with 2 parts mineral spirits to 1 part varnish makes hand applying the stuff easier, but increases the number of coats you will eventually need to apply. by two -three times.
One other poster noted that open grained woods like walnut, ash, oak and hickory may not sand perfectly smooth no matter what you do, and that's true. To get them piano top smooth requires filling the grain with a wood filler (not to be confused with the glue-based wood patch available at any hardware store). Wood grain filler is designed to fill the pores of the wood without adversely affecting it's appearance. Typically you will match the filler color to the wood type. Woodcraft stores and mail order carry a variety, so do many other specialty woodworking stores. Once you fill the wood, then you start finishing, usually with a film type finish like varnish, lacquer, shellac, etc. For a hard use item like pistol grips I would definitely look toward varnish type finishes and maybe true oil.
Film finishes don't need you to run the sanding grit up as high either because the film itself will build into the scratches and small pores, bridging them over and producing their own surface sheen. Sanding over 220 grit with film finishes is pretty much wasted effort.
Water-based polyurethane is not as durable as oil based polyurethane, its also not as warm since it doesn't amber up the finish. If you want to maintain exactly the same color on your project, water-base may be just what you are looking for though.