I'm answering solely based on my personal experience as a native speaker. I would say they are all perfectly synonymous. The only difference is placement in the sentence. "Nevertheless" and "nonetheless" can appear at the beginning of the sentence or directly after the verb, really most anywhere, just not at the end. "However" can be placed virtually anywhere, as long as it's not in the middle of a noun phrase or something like that. He was nevertheless/nonetheless pleased with the result. Nevertheless/nonetheless, he was pleased with the result. He was pleased, however, with the result. However, he was pleased with the result. He was pleased with the result, however. All of these are acceptable. It should also be noted that "however" is much more common than the rather archaic "nevertheless" and "nonetheless," though they are indeed used and you wouldn't get funny looks for using them. Hope I helped. :)