When Avast! (Free) is running, I am unable to post to Usenet with PowerPost.
What error messages are you getting ?
I assume that you can send and receive pop3/smtp email normally ?
It may be the fact you are using PowerPost (I haven't used it, so don't know how it works or what it covers email.news, etc.) and that adds another layer and need to be integrated with the web shield proxy. There are other news readers that work with avast but need tweaking, so a forums search might return some relevant info.
In the mean time you could try disabling the Internet Mail provider which monitors NNTP traffic or disable the NNTP scanning, that way you aren't disabling other on-access scanning.
Or you could just have the mail scanner ignore the PowerPost executable (whatever it is). By editing the avast4.ini file, [MailScanner] section using a text editor like notepad. It is best to save a copy of avast4.ini to another location in case of any problem, you can then copy the original back.
[MailScanner]
IgnoreProcess=PowerPost.exe add this line if you don't already have an IgnoreProcess line.