There's a two-stage system by Selleys called "All Plastics" which has yet to fail me when gluing plastic to plastic. It consists of a felt pen primer, used to prepare the two surfaces, and the glue itself which is very much like cyanoacrylate (superglue).
I've done head-swaps on soft plastic figures from Revell, Airfix and Strelets with this stuff, using a simple butt-joint (no pinning or anything) and got a join strong enough that I can swing the figure around by its new head without the join parting.
As far as gluing soft plastic figures to a base of another material, a gap-filling glue that you can use to encapsulate the figure base works, even if the glue won't stick to the soft plastic. Just use a toothpick or something to push a strap of the glue over the figure base, between its legs, from side to side. Or even just push the glue up over the edge of the base slightly, so that when it cures the figure is held in place. Plain old white glue will usually work, but I prefer 5-minute epoxy, or superglue sprinkled with baking soda.