First check if your server is an open relay: http://www.spamhelp.org/shopenrelay/
Originally Posted by still_(0)_(0)_awake
I believe has hacked into my email server and is using it to send out emails from “firstname.lastname@example.org” among other email accounts. These are not valid ones that I use.
Make sure all your web appplications are up to date. This looks as if someone is using a whole in an app to send emails. Which distribution do you use?