Oily headboard

I just inherited a gorgeous bedroom set from the '30s, very art deco and made of some kind of “blond” wood. Everything’s in excellent condition, except for the bed’s headboard. It has large dark head-oil stains that accumulated over the decades.

How would I go about removing the oil, restoring the headboard to its original color?

It is doubtful that anything short of complete removal of the existing finish will restore it to it’s former beauty.
You might find it profitable to consult with a professional refinisher.

I don’t know if you are wanting this for it’s value or not, but a lot of times removing the finish from a piece of furniture will lessen it’s value.

Not a solution but a comment-if the original finish allowed oils to pass through and the wood itself is darkened, simple stripping won’t restore a uniform appearance. Seconding the advice to seek a professional furniture refinisher-you could send your question to Joe L’Erario and Ed Feldman: http://www.furnitureguys.com/about.php

Before you start stripping, I’d try using some shampoo and water to get the stains out. Let it soak for a bit. I did this with a wooden sofa arm years ago and it worked. YMMV.

If you aren’t necessarily worried about messing with the finish and lowing the value, you could always try wood bleach .

I would try some Murphys oil soap . FWIW they have an FAQ section on cleaning wood.