You need to comply with that quote you made as avast can't intercept and scan encrypted email. By unchecking the SSL options in your email client avast will be a) able to scan the email and b) it will handle the secure connection side.
In OE, Tools, Accounts, select the two problem accounts (one at a time), right click on it and select Properties. From the new window, Advanced tab, and uncheck the This server requires a secure connection. In the Server tab, ensure that you also uncheck the 'Log on using Secure Password Authentication if it is enabled. Repeat for the other account.