Wood – Removing sap from an old railing

By "White spirit", do you mean turpentine or mineral spirits? If that had no effect on it... My best guess would be that it's improperly cured polyurethane, or water-based polyurethane that wasn't mixed properly. Additionally, polyurethane doesn't take to pine well and is pretty resistant to being removed chemically, so there's another pointer in that direction.

You can try denatured alcohol. If it comes up with denatured alcohol, it's probably improperly mixed shellac.

What I'd probably do if I were you would be to sand it down completely back to bare wood, first with 80 grit and then 120 and 220 grits. I know it's a pain in the butt, but it'll provide the best finish overall. Then stain it and finish it again with something that isn't polyurethane... if you stain it, I'd recommend a lacquer finish like Deft, and then a really nice set of absorbent coasters so that you don't keep getting the surface wet. ;) Or if you do use polyurethane, use a satin spray in a rattlecan and bring it indoors to a moisture and temperature controlled environment to cure for 48 hours before you put it back into use. And your last option would be to paint it (after sanding back to bare wood, or it won't adhere!) with an oil-based enamel and a bit of penetrol.

It's a little difficult to say that it will be a definite fix but a great start would be refinishing the inside of the cabinet. While I'm sure its possible to re-stain and seal the inside of a cabinet that just seems like way too much work so I'd stick with painting.

I found this nice article about painting cabinets if you want some design ideas. The process shouldn't be all that involved. You'll probably want to sand first and clean the shavings out well then give it a nice coat of whatever color you decide to go with and let it dry. Pretty much like painting any other piece of furniture, just a little bit more of a pain to get inside there.

I once stripped and painted all the drawers and cabinets on a work truck and that was a real pain. Luckily I was able to use a paint sprayer so that made it a heck of a lot easier. If you know someone with a paint spraying system beg them to use it and the finish and coverage in the tight areas will be wonderful.

Just my $0.02 and I can't say that this will be a definite solution but I can't imagine a wood smell getting through a through coating of paint. If your really worried you could use some thick outdoor paint that's designed to work as a sealer too. Best of luck with your project, post pictures if your need help along the way!