Based on those pictures you should be able to use your Japanese PSU (100-127V~3.7A,47-63Hz 135W) in the US to power either your Japanese Xbox 360 S or your PAL Xbox 360 S.
You can use your Japanese Xbox 360 S
where you are right now with the Euro PSU (200-240V, 47-63Hz 135W).
Now video-wise the Japanese Xbox 360 S is fine with US equipment. I'm not so sure about the PAL Xbox 360 S - that might be an analog (composite, S-video, component) vs. digital (HDMI) output issue.
Apparently you can force a PAL Xbox 360 into 60Hz mode (PAL60):
http://www.youtube.com/watch?v=6-IEsnhwC5A
though it seems that the setting may only be accessible while the console is connected via composite video.
After you force the console into 60Hz at least HDMI and VGA video should work on most US equipment.