An easily available and inexpensive glue in my area is E6000. (W Mart, Hobby Lobby, etc.)
Once setup it seems to be stronger than the wood it's bonded to.
It's similar to Goop and Uhu glues, but seems to have a stronger bond, and gets a bit harder.
I'd test it on plastics before real use. I've had no problems,
but you never know.