How can I remove transformer windings from wooden template?
I would cut both sides off, one only close to the edge, maybe drill some big holes, and split it with a BF hammer and a chisel. 

You could also try whaling on the longer end with a dead blow hammer to try and shatter it after drilling the holes. 

Personally, I have a small benchtop 12 ton hydraulic press that would be more controlled or a 3 ton arbor press (that might not be strong enough). A big C-clamp or large bench vise might work just as well, but leave enough room on at least one end to get ahold of the 2x4 or you may actually make things worse!

I think oil or soapy water would just make the wood swell. 

Your PVC jacket is probably good for about 90°C (but do check the rating on the markings) so you could try leaving it in an oven for 24 hours (or enclose it in an air tight box with fresh dessicant from the hobby store) to dry and shrink the wood. Drilling it first would make that process faster. An hour or two in a vacuum chamber might also do the trick (again, drilling the center out would expose more wood).