Rambling reply...
I'm aware that you're asking me for the command to disable outbound mail. In this case, there's no reliable way to do that. Shut down the server. That is how you deal with these problems. This has unfortunately already been going far too long. Hacked? I'd kill the whole server. Everything. Immediately. The longer these cases drag on, the worse the messes tend to get, and the more blacklists your server gets onto. Once shut down, I'd isolate the box, image it, and then start to investigate the damage — that's not a quick process, either — from another box using Target Disk Mode or swapped disks.
If your mail server box is hooked directly to the Internet and with no intervening firewall box that you can control, then I'd just shut down mail entirely, and troubleshoot and clean up the mess. Quite possibly the whole box, as described. To allow arriving mail to continue, redirect your DNS MX mail record to a different server using your public DNS, either with that server operating as a lower-priority relay server and caching the mail there or — probably better — replicate your accounts with wholly new passwords and host your mail offsite temporarily.
It's common to assume that everything about this breached server is now not trustworthy, too. Not until the breach has been identified and isolated, and — if the box got rooted, as can happen — the entire data contents have probably been exfiltrated, and the programs and settings are not trustworthy, and you're headed for a nuke-and-pave / wipe-and-reinstall sequence. Backdoors and changed passwords and new accounts can and do happen. (Some background on hacked servers.)
There's no easy and no quick way to deal with this, and one of the nasty things with a not-DMZ'd public-facing and rooted server box is that your whole internal network and Wi-Fi passwords and the rest may well all also be toast. How far the attackers got, that might be clear from the logs, or it might well just be safest to assume the worst. That is, nuke-and-pave the box, restoring from either pre-breach backups — if the attacker hasn't hosed those — or from distributions. Alternatively, it's also possible that some box elsewhere on your internal network was compromised, and it's that box that's spewing out spam, either through your mail server or directly.
Without details and without investigation, the extent of what happened is not known.
pf — links referenced in an earlier reply — is the path for shutting off network connections, but — if the attackers got further than this box — then some random network printer — yes, some network-connected printer, I'm not kidding here — can be sending out spam. This is part of why having a firewall — which is not a panacea — can help. Here, your firewall — your OS X Server box — has been breached. But if you trust it, shut off both inbound and outbound TCP port 25 traffic.
As for NAT, I use firewalls with embedded VPN servers. FWIW, NAT itself is not security; it's the port-forwarding settings and the ability to isolate and restrict unnecessary traffic through to the public internet. I'd use a firewall — again, not a panacea — with even a network using public addresses.
As for the logs, the locations on those vary. Console.app can get you a view into the basics, but beyond that you're using the command line. In Mountain Lion Server, look in /var/log and /library/server/Logs and /Library/Logs and a few other paths. Mail.log is at /var/log/Mail.log, but the various logs have moved around in recent OS X Server releases. To find logs, you can control-click on the log name in the left column in Console.app (select Show Log List, if necessary) and choose Reveal In Finder from the pop-up, or you can use that path to locate and read the logs via the command line and Terminal.app.
FWIW, ZyXEL ZYWALL USG is a local favorite and a very capable box with a consistent interface, DMZ and VPN capabilities, but those products are not "introductory" products, They most definitely do assume familiarity with IP terms and concepts and mechanisms. Other than having purchased various gear from ZyXEL, I have no connections with them.