What is this soft, sticky wood finish and how do I remove it?
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.