Removing black stains from oak will require refinishing and scrubbing of the wood. If the marks are contained in a small area, then the refinishing is only needed for that small area.
Black marks appear on oak when moisture has penetrated the finish and damaged the wood beneath. The only way to remove stains is to strip the finish and treat the oak. Once the finish has been removed, dampen the area with a wet cloth. Then, using an old paint brush, apply several coats of bleach to the stain. Let it soak for a few hours, and then wipe away any moisture and reapply. Let the bleach soak overnight. Wipe and rinse the area to remove any remaining bleach and allow to air dry completely before refinishing.
If the overnight soak did not remove the stain, a wood bleaching product will need to be used. These are available at most hardware stores and come as two separate liquids that will need to be mixed. Again, moisten the area with water, and then apply the wood bleach with a brush or sponge. This will need to sit undisturbed for about 4 hours. When it starts to bubble, it is working. After the 4 hours are up, be sure to neutralize the bleach with a vinegar wash of two-parts water one-part vinegar. This will keep the bleach from causing damage to the area. If the black marks are on an antique wood item, this process will decrease its value.