Neither is common. But among speakers of a certain level of education, "it avails me nothing" means that doing whatever "it" refers to has resulted in no success, no progress, no results of any kind. The exact phrase "it avails someone nothing" sounds extremely awkward, but "if avails him/her nothing" is OK. Even squeezing a name in there sounds odd. Like, "It avails Alex nothing to try..." Possible but strange. The most common usage is to refer to oneself.