Most likely that these mails don't come from the actual AOL account but from some other machine/user who got hold of your email address. May take a look at the email headers to proof that. Well, it's quite a common issue, this is what we tell our customers in such cases:
Such side effects happen due to some limitations of the protocol which is used to send messages through the internet (SMTP - Simple Message Transfer Protocol). It's actually designed to work like the traditional post: Put a letter into the post box and let the post transfer it. Nobody will ask for authentication to proof, whether the person, who puts the letter into the box, is the same as written as sender on the letter - basically everyone can send a letter with a phony name on it. The same happens here: It's technically possible to use any existing or even phony email address.
To avoid sending faked mails, most providers have special workarounds implemented. Unfortunately often malicious code (worms, viruses) installs independent SMTP servers on infected machines to bypass such methods, some SMTP servers around the world are 'open' and offer mail routing services without any checks. Often the persons who own such machines doesn't even know that their infrastructure is misused, but the hackers identify those quite quickly. The addresses are mostly collected via Virus, Worms, etc. from Windows applications such as Outlook, Addressbook or even Excel lists but also can be collected from public web services, such as forums or normal web presentations.
If you get delivery failures for messages you never sent - this is for you:
As an email message always contains a sender (From field), any delivery failure or status message will be sent to that, even if the original sender was somebody else.
The good thing on email is that the header information also contains a lead to the real sender or at least a server which was abused. Thus it's possible to proof that a message was not sent from your account, technically it's possible to identify the real person or at least the affected PC. In some re-occurring or legally critical cases it would be recommended to take action, but this of course is very time consuming, involves 3rd party resources and often requires action from legal authorities.
Hope it clarifies,
best regards - Dirk