My guess would be that your server is configured as an open relay. Have a look at your relay settings (in the Administration program, go to Servers / Localhost / Connectors branch, open the properties for "SMTP" and go to the relay tab) and see how you've got it configured. My default MailEnable requires relaying senders to authenticate. You can allow local senders to relay unauthenticated and to allow IP ranges to relay unauthenticated. The first of those options allows any spammer to forge a "From:" address as one of your users and relay successfully so, generally, it's bad news.
If you're only allowing authenticated relaying then someone may have had their credentials compromised.
SMTP protocol logs, kept in "C:\Program Files\Mail Enable\Logging\SMTP" by default, may help you track down the source of the messages. Consider looking there, too.
If I'm misreading you and you're saying that messages are being sent but aren't hitting the logs then you're probably hosting some malicious software that's sending messages w/o going thru MailEnable. That's always a possibility, too. Look for unexpected processes running and unexpected SMTP traffic that doesn't correspond to logged traffic from MailEnable.