The olive oil will help in retarding the oxidation/sulfur migration only.
You need to remove the oxidation first!
That's another story all in it's own right, lot of threads on getting the thing back to black.
About as many different methods as there are pipers!
Personally, I use Micro-Mesh sanding pads, all 9 grits. Keep the pads and the stem wet while working on it.
Dry the stem in between grits to check your progress. A really bad stem will take me about 30 minutes but when done it looks like black glass. I protect and prolong the shine with either carnauba or Paragon.
These are the sanding pads I use, the 2"x2" set at the bottom of the page.
Micro-Mesh