Contrary to various urban legends, Japanese does have a word for "No", however, it appears it's extremely rare to hear it used directly, given the connotation of impoliteness of "iie". Even factual questions like "Is your sign X", are answered with "chigau" when one's sign is not X.
I'm completely new to Japanese and I'm trying to figure out how many ways there are to express nuances of "yes" vs. "no".