I would give them a bit more time, sand them lightly, and apply a sealer coat of shellac. Then proceed with your poly. Poly does not stick well to waxy or greasy surfaces, but shellac will provide a good barrier coat. Be sure to use a DE-waxed shellac.

Here is a link that might be useful: Seal Coat 100% dewaxed shellac

Wipe down with paint thinner to remove as much oil as possible.
MEK would be even better.

Thanks to both of you. I'll start with brickeyee's and if not better by Friday I'll go with some sealer.

Tsk, tsk. Thats what you get for letting the dog cook with olive oil. ;-)

Clean as much of it as you can off, using something that will dissolve oil. I'd try to soak up as much as you can. Since its a drawer front, I'd take them out and try putting some kitty litter on to absorb the oil. This works well for garage floors. Let it sit for a day or so. Get as much of the oil out that you can.

Then seal over it. An issue is that vegetable oils like olive oil can go rancid. They don't cure. So if you can, you want to get it out rather than leave it in the wood.

John

This might be the time to consider using an oil finish rather than poly.

I finished an old rocker that someone had used the seat to store a lawn mower engine on. Cleaned it up with a lot of lacquer thinner, sanded and used an oil finish. It turned out beautifully.

I know this was a long time ago, but I just poly-ed my drawer fronts last weekend. The oil pretty much either soaked in or evaporated, because there are no marks anymore. Yippee! (And now I forbid me dogs from cooking in the kitchen and hide the olive oil. LOL!)