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.

You would have to travel back in time a hundred years or more to hear this expression commonly used. We could say ‘it’s no use’ [doing something], ‘it’s no help (to me) [to do that] or ‘it’s useless’.

The only remnant of this outdated phrase is "It was to no avail" means it was a waste of time, no point, without success. I tried to reason with him but it was to no avail. you may still hear it expressed in this form very occasionally by educated people.

Other possibilities: It didn't help at all. It did us no good. It didn't benefit us. It had no effect etc.

"It was a wasted effort." "My attempts didn't amount to anything." "Anything that we tried was fruitless." Of course, structure the sentence based upon the situation.