What 120VAC devices can take 150VDC?
If its internal bus rail (prior to the final switching stage) is 150 volts DC then, when feeding its bridge output it would be able to generate possibly up to 300 Vp-p or a sinewave of only 106 V RMS. This tells me that it's not a high quality device because, to achieve an RMS of 120 V, would need an internal bus rail that is a about 50% of the peak-to-peak of 120 V = 339/2 = 170 volts DC.

Basically what I'm saying is read the small print because it may just be a square wave converter and possibly incapable of delivering enough voltage to some 120 V AC appliances. It may even cause problems with other appliances due to the harmonics.


  How can I tell what black box device normally rated for 120VAC can
  take 150VDC?


That is difficult because it's not normally stated. Given what I said above I would look at a few other inverters and read the details in the spec sheets. If details are not available then I would be suspicious of its usefulness.