avast isn't a firewall so doesn't block ports, if those ports are using http protocol over port 80 then the web shield would scan it, other than that it wouldn't be scanned.
If the ports used are commonly used as exploit (DCOM, etc.) entry points for viruses/worms (but those given don't appear to be) then the network shield might monitor those ports, but again it is scanning not blocking.
What is your firewall?
What other security based software do you have installed ?