The oil finish can have many names, from countries, ie French, Danish, Dutch to brands. Basically cleaning oiled wood requires you blend: 1 pint boiled linseed oil, 1 pint gum turpentine, and 6 oz. distilled white vinegar. Gum turpentine is flammable but smells like fresh wood. Wear gloves. Do not use around flame or spark; do not get on skin. Wipe the surface with a soft cloth that has been dipped in the cleaning solution. Never pour the solution directly onto the wood. Let the solution stand for a few minutes to loosen the soil; then wipe off the excess. All excess oil must be removed or it will attract dust and get gummy or tacky. To finish, rub with the grain.
NEVER USE wax or furniture polish on oil finishes. Re-oil yearly with boiled linseed oil, tung oil, or a product recommended by the manufacturer. These oils harden when exposed to air and seal the wood. Never use non-drying oils like mineral oil for wood finishes for furniture. Avoid using an oil dressing too often or too liberally as it will cause a hardened oil build-up. If this happens, use mineral spirits (paint thinner) to dissolve the residue.