I guess if it were my furniture, I would try to remove as much of the greasy/sticky stuff with something like mineral spirits or acetone. Then I would use a repair crayon on it in a matching color. You can buy them in hardware stores where they sell furniture refinishing products.

Ace hardware has some nice repair kits.

I'd find a vase or flower arrangement big enough to cover all three spots. Like I have a hand-loop rug my sister made in the family room where the ink spilled on the carpet.

I operate a furniture repair co. There is no easy DIY solution to this problem. Do not use Acetone, as it will eat through just about any finish in a second.

For large areas, strip and refinish is the solution, particularly if there is any color loss.

You might try getting some lacquer-based touch up markers to color in the area. This will make it less noticeable to "a man on a horse galloping past at 50 feet away." Don't use Minwax that is just "stain in a pen" because it does not have enough binder in it and will rub right off. Lacquer based, such as Mohawk or Guardsman, will bite into the finish and bond with it.

I had a similar thing happen, only I knocked the scented oil over with a bare floor vacuum cord. When I went to wipe the oil off, the black varnish wiped off too. Thank you very much for the advice.