For stock clean up, use Murphy's Oil Soap if there is LOTS of grime and old flaking varnish. Scrub using a washcloth over and over until the cloth no longer picks up the black stuff. Use a toothbrush to scrub out the checkering. Murphy's Oil Soap will remove varnish, so use with caution.
Another option for cleaning years of gunk from a stock is Meguiar's Fine Cut Cleaner followed by Mylands Friction Polish (available from The Wooden Post) to restore the finish.
If you want to clean, but not remove any of the old finish, use Meguiar's Cleaner Wax Paste, Birchwood Casey Stock Sheen & Conditioner, Formby's Buildup Remover, or Kotton Klenser. Apply with a washcloth until the washcloth no longer picks up the gunk. Then use Formby's Lemon Oil Treatment or Old English Lemon Oil to put some life back in the wood. Dr. Drew uses Old English Lemon Oil about every 6 months in the desert because of the low humidity. Let the Old English Lemon Oil dry then use Johnson's Paste Wax, Trewax or Renaissance Wax (available from Woodcraft or PicreatorEnterprises Ltd. ) Howard Feed-N-Wax can be applied regularly to protect the wood and finish also. It's amazing the color and contrast that will come out after a serious cleaning!
If the barrels have not been cold blued, you can safely remove most of the corrosion on the barrels using Kleen Bore's Formula 3 Gun Conditioner, WD-40, Mothers' Billet Metal Polish, or Blue Wonder Gun Cleaner and OOOO bronze wool.
For the receiver (where the case colors are already worn off) use an all copper penny or a 3M Scotch Brite pad with Kroil (available from Kano Laboratories) or Kleen Bore's Formula 3.
Flitz will clean the metal but WILL remove case colors and blueing.
Naval Jelly, Evapo-Rust and Certanium Ox-Away will remove RUST AND BLUEING.
Ballistol was designed for the German Imperial Army in 1905 and it is safe for wood, metal and leather. It is mineral/soy bean oil based and therefore will not soften checkering. For severe plastic fouling in the bore, use Ballistol with a bronze brush wrapped in 4-0 steelwool and attached to an electric drill.
EEZOX® Synthetic Premium Gun Care is a relatively new product that is an excellent metal cleaner and protectant. It protects metal surfaces from moisture, salt, finger prints, and blood, and also darkens blued barrels that have turned ‘plum’.
Great care must be taken cleaning case colors. Dr. Drew uses Flitz Gun Wax to both clean and protects. Case colors are lost primarily by abrasion, but some oils and chemicals also degrade CC, especially if acidic or alkaline. Dr. Oscar Gaddy used Behlen's to protect CC; others recommend thinned TruOil.
It is certainly reasonable to protect the colors and metal with a quality wax such as Johnson's Paste Wax or Renaissance Wax, especially if the gun is exposed to salt water.
To clean corrosion from the engraving, get some 14-18 gauge solid household copper wire like Romex. Strip the insulation off of one strand and cut it at a long angle with a pair of diagonal cutters. Use the cut end as your 'pick' or tool along with Kleen Bore Formula 3 or Ballistol to remove the rust. If it gets worn smooth or rounded, just nip a small increment from its end to 'resharpen'. The Formula 3 will penetrate and loosen the rust as well as prevent future rusting, and the copper 'tool' will not scratch the engraving. It will be tedious work, but you should only need do it once. You could put a gouge in the wood though if you slip, so go slow. Use a piece of wire long enough to be held comfortably in your hand and bend the last ½ inch 90 degrees.
For the best thing to re-oil or wipe down engraved surfaces, get a piece of real lamb's wool leather that has been clipped close. There is simply nothing more effective to insure you get a coat of oil on and into the engraving. A small piece will last you a lifetime.
To clean up and rejuvinate that classic leather Leg-O-Mutton case:
Pecard Classic Leather Dressing
Connolly Hide Care Cream