Socks are two dollars a pair, A pair of socks costs two dollars.

#1 is ambiguous. It literally means each individual sock costs two dollars. However, in the United States, socks are always sold in pairs, so the listener would probably assume it means two dollars for a pair. In real life, the listener would probably ask "Do you mean two dollars for a pair?" In #2, "each" is not right. I would say "socks are two dollars per pair." You could also say "socks are two dollars for each pair."

“Two dollars a pair” is the way we usually say it.

Both are correct but the second would be better as you are referring to a pair of socks, not just one sock, as the first sentence would imply. If you said the first one, most people would probably still think of a pair of socks not just one singular sock, but to avoid any misunderstanding, using the second one is better.