Hi,
Make sure your logs are set to detailed, then look at the header of one of the emails, get the IP address from the header, and search your SMTP logs for that IP and date range. You should see how the are authenticating from the logs, usually authenticated and authenticating are key words.
Make sure you do not white list smtp IPs much, and it isn't opened for a large range.
SmarterMail is up to v14.4 now, you might want to install the latest updates, to have other fixes.
Check SMTP Authentication bypass, make sure you do not have a big range in there too.
Besides of course checking under Protocol Settings -> SMTP IN -> Allow Relay = Nobody
Good Luck
-dave