There is no solution to copy your emails as a text, just because (in many cases) emails are more than just text, they contain photos, attachments, etc. If you want to have off-line copy, you'll need some email client which can import all these messages off AOL.
Some good email clients: Mozilla Thunderbird, Microsoft Mail (many versions depending on what Windows version you have), Microsoft Outlook (if you have any of these). Configure the client for POP3 retrieval. If I was you, I would create first an archive on GMail. and pull all from there.