How can I determine the amount of insulation in a wall...

Q: …without tearing the wall open. Is there a device to do this?

A: You can make an educated guess. I don’t know of a device

A 2x4 wall will usually have R-13 if anything. (No idea how old the house is). You can take the cover off of an outlet and see if you can pull some out from the gap between the drywall and the box. A phone jack would work best as they’re often installed in just rings and not full boxes. There could be some more exotic insulation (i.e. the sprayed in expanding foam) that would be more difficult to track down the actual R-value.

Then you need to figure out if the house was sheeted with foam that could provide more insulating value…