Is there a resistance test or something I can perform to check?
No.
But you can look at the current they draw and compare this with a non suspect one.
why are they sensitive to having one supply plugged in before the other? What kills them when this happens?
Over current kills them. The circuits latch up, that is they do not act as transistors but conducting diodes. Some devices like OLEDs have three or four supplies that not only must be brought up in the right order but also within a strict timing.