In my opinion the most correct is e-mail. It seems to me that mails are totally inappropriate to use. When it comes to messages, I believe it is a matter of opinion.
Personally, I have encountered e-mails several times as answers to e-mails I have sent to different persons and firms. For instance, Ladbrokes, wrote me an answer to two e-mails I had sent it, and that 'mail' (for some reason I think it sounds right in this situation) started like this;
In response to the two e-mails you have sent us.....................
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