While your question might get better answers in a wood turners forum, I will move it to ARG for comments by some turners and woodworkers here.
The methods of removing stains from wood depend on the source of the stain, as well as the finish on the wood. Simple dirt and grime can be washed off with soap and water and the wood dried. Solvents may be needed for oils and greases. The finish may need restoration or removal in other cases.
A simple first cleaning attempt is to wipe it off with a damp rag, then with a rag moistened in denatured alcohol. If that helps, let dry a bit, and rub with 0000 steel wool. That will restore the look in a lot of cases. A new coat of surface wax or other finish may be needed if you have to sand or rub away the old finish.
Oak has tannins, and any contact with steel, iron, many metals, hands that work with those things, and many chemicals can turn it dark. If that is the case, the discoloration may be permanent. The steel wool treatment will still restore the shine to the wood, though.
