The avast firewall works in conjunction with the other shields, but as far as unauthorised outbound connections go that would down to the firewall as it would be pretty hard to determine if the connection were malicious.
That is where the other shields come in if you had a hidden/undetected spambot on your system, the mail shield monitoring the email ports (before it gets to the firewall) could identify the multiple identical emails. The likelihood is that it also wouldn’t be using your email program (most have their own very small SMTP function), that could be an unknown application or one that hasn’t previously been authorised for outbound connections. Here the firewall might come into effect.
So there are multiple checks that would hopefully pick up on spam being actually sent from your system and why my guess that your email address, not email account, or your ISP would likely be contacting you also.
In all honesty, you don’t want to be downloading 1500+ emails just to filter them (aside from the fact it could take ages on dial-up), then you have to delete them. I don’t use Outlook, so I don’t know if there is anything that would allow filtering/deletion at email server level (but I would doubt it). It would totally depend on how much of a pain in the rear it is and how much time it takes to deal with each day, as to the benefit of having a program do it.
If you haven’t already got this software (freeware) for a secondary scanner/opinion that your system is clean, download, install, update and run it and report the findings (it should product a log file).
MalwareBytes Anti-Malware (MBAM), On-Demand only in free version http://download.bleepingcomputer.com/malwarebytes/mbam-setup.exe, right click on the link and select Save As or Save File (As depending on your browser), save it to a location where you can find it easily later.