I suppose you have Postfix as your mail server, (in any case you should when asking this kind of questions give more info, like OS, mailserver, versions)
but the important thing is that your have i quote:
PASS Open relay test OK: All of your mailservers appear to be closed to relaying
relay is the property of a mail server to restrict who (ip, user, Mailclient) can receive and send mails (not the best definition but sufficient), so in the postfix main configuration : main.conf
you can enable or disable this restricctions. There are a set of rules, open them and try them each one, so go search google.
be careful becouse if you open all the restricctions you can be matricaulated as an open relay server and others servers may not receive mail that your server sends.
I think the success of a mail server is a good set of relay rules and a good set of antispam procedures. (sometimes relays rules prevent spamming )
hope this helps, anf good luck