Put several drops of water directly into the scratch. Let the moisture soak into the wood.
Cover the scratch with a clean cloth.
Set the iron to warm and iron over the cloth gently. Heat and moisture can serve to eliminate a scratch by making the wood swell and expand. Do not use the iron's steam heat setting.
Apply a coat of petroleum jelly, butter or mayonnaise to the scratch to restore the oak's color. Let it sit overnight. The next morning, buff the wood in the direction of the grain with a clean cloth. In most cases, this will remove the white appearance of damage. This method is also effective for water marks.
Apply a fine-point black laundry marker to hide scratches on dark oak; use iodine or a fine-point red marker for red finished furniture. Shoe repair shops carry a wide variety of shoe polish and dye colors that can be used to match wood color.
Apply neutral furniture polish to erase scratches on lighter-color oak pieces.