Hello -
On plastic, I have used the thickest grade of ACC adhesive (superglue). It fills gaps and sets a little more slowly so you can make last minute adjustments. After it is down, check the edges and if necessary secure with a bit of glue on the tip of an Exacto knife.
I have also used .005 styrene for this purpose with some success, though you must be more careful because it is easy to mar the surface.
If you are gluing styrene to wood, I would use Walthers Goo or other contact type cement. The reason is that wood is subject to a lot of expansion and contraction due to moisture conditions; you might find that the plastic spalls off if there is a big change in humidity.
Good luck!
BRUCE CLOUETTE