Moisten a sponge with water and heat it in a microwave oven for 40 seconds. Put on rubber gloves and remove the heated sponge from the microwave.
Spray a small amount of citrus cleaner on the sticky substance. Rub the cleaner gently with the sponge until you have removed the stickiness.
Wipe the cleaning residue off the wood with a damp cloth and buff dry.
Sprinkle cornstarch over a damp sponge. Rub the wood gently with the side of the sponge covered with cornstarch.
Wipe the antique wood furniture clean with a damp cloth. Continue if the stickiness remains.
Apply a light layer of white vinegar to the remaining sticky residue, and rub gently with a sponge. Rinse with cool water and buff dry.
Wear rubber gloves. Pour mineral spirits into a plastic container.
Dampen a cloth lightly with the mineral spirits, and rub the sticky film off the antique wood.
Continue until you have removed the sticky residue. Wipe the antique wood furniture clean with a soft cloth dampened with water, and buff dry.