Dose earning LLM degree in online/distance study　course(that the ABA "acquiescenced to") satisfy the requirements to sit for ANY state bar exam? I have JD in Japan.

Every state bar exam is different and each state has it's own requirements for examinees. Only a few states allow foreign qualified attorneys to sit for the bar after meeting specific conditions. Examples off the top of my head are New York, Massachusetts, Tennessee, California and I believe Minnesota or Michigan. The best source of information is the state's bar examiners office or call the local Bar/Bri office. www.barbri.com
Good luck.