Yeah, I guess my post only answered this question:
Is this normal? And for what purpose is that?
Shouldn't we let him try running the usual?
http://malwarebytes.comhttp://superantispyware.comDownload those, make sure to update them, and run a quick scan (quick scan for malware bytes will find 99% of problems without a long wait).
If those don't work, then I'd suggest running "netstat -a -b" to see what port svchost.exe is using, and where it's going.
If that's not enough information, use a network scanner like ethereal.
However, I highly doubt that "Avast!" is the one making svchost make internet calls. Unless of course Avast uses svchost to update it's definitions.
Is it that much to worry about though? As long as your system is clean by 3 different programs, SAS / MBAM / Avast then I would think if there was something accessing the net, it's probably legit.