How can I stop the random "mail delivery failure" emails I receive from unknown addresses?

Firedog, you didn't answer the original question... (How can I stop the random "mail delivery failure" emails I receive from unknown addresses?)

You can't. Mail servers around the world are trying to deliver messages purporting to come from you. If they can't deliver for one reason or another, they helpfully send you a message saying so and explaining why. If you didn't send the message that bounced (i.e. it's not in your Sent items folder, neither locally nor in webmail), you've nothing to worry about. Delete the Delivery Status Notifications (DNS) and forget about them, having made sure that the DNS does in fact refer to a message you didn't send.

That was very bad advice from your ISP. A notification like that is telling you that a message sent from your account, or at least with your address as the sender address, was not delivered to the addressee. If you didn't send the message, then probably some criminal did.

You should examine the message to see the details of who sent the message to whom. It means that either your own account has been compromised and that someone else is now using it to send spam (or worse), or that your address has found its way into the hands of spammers who are now busily sending spam (or worse) in your name. Getting these notifications may be annoying to you; it's just as annoying, if not more so, for those who are receiving unwanted messages purportedly from you. 

Noel