Every known living organism, extremophile or not, needs liquid water to live. Some microbes may survive high radiation in vacuum for a long time, but they're dormant. No microbe can be active on the surface of these moons or even on the surface of Mars, but if they manage to dig deep enough and find liquid water...

BTW, lack of oxygen is not a problem. In fact, oxygen is toxic to all lifeforms on Earth. Some, including us, have found a method to make use of it, but it still destroys our tissues causing aging.

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Science is a way of trying not to fool yourself. The first principle is that you must not fool yourself, and you are the easiest person to fool.
-- Richard Feynman