Ted,
It sounds like Avast is holding Port 25 and 110 open to scan OE email, but I would bet that OE is not configured properly.
Shut down OE, run the Mail Protection Wizard in the Avast program folder and then start OE again.
This NORMALLY fixes this problem. If it does not, then we need to find out what program is holding open the ports that Avast needs.
Also, look in the OE, Tools, Accounts section and check on how the server and POP/SMTP servers are configured.
Server should be set to 127.0.0.1
POP should be something like yourusername#incoming.isp.com
SMTP should be something like
yourusername#outgoing.isp.com
Later.

Ok?