"Inexplicable and unexplainable are mostly interchangeable—both describe things that can’t be explained—and using one in place of the other is never a serious error. They have differentiated slightly in modern use, though. Inexplicable tends to describe things that are seemingly without logic, especially human actions, feelings, and creations, but also other things that one can’t explain in rational terms. Unexplainable tends to describe nonhuman things, especially natural and supernatural phenomena, and it is also used for human things that are difficult to explain but not necessarily irrational.
"In other words, while inexplicable things have seemingly no logic to them, unexplainable things are just very difficult to explain. In fact, unexplainable could often be replaced with unexplained with little loss of meaning.
"This differentiation is new, however, and not deeply engrained in the language—it is much in evidence in recent news and blog writing but less apparent in recently published books—so it will be interesting to see whether the words continue to grow apart in the coming years."