Two outlet stopped working after turning on electronic cauterization device
I would turn your breakers off to those outlets and remove the outlets, I believe you will find a bad connection in each outlet probably a back stab. But could be a loose wire nut or broken wire. When this usually happens it is with a heavily loaded circuit , but your 120v load is only about .2 amps. With this device being a 2 wire a surge type power strip really won't make any difference. 
To be able to use a wide voltage input with a specific output it is probably a switching power supply that had some kind of fault that after the second attempt cleared an internal short (I would not use this adapter for risk of fire knowing this).  Power strips that have surge supressors work by a device called a metal oxide varistor, these devices dump excessive voltage levels or spikes on the power line to ground. So as I said I would toss this adapter because there is possibly some loose solder floating around or some copper traces from the printed circuit that caused the original problem to your home wiring.