Cannot remove Trojan.ZeroAccess and Trojan.Gen.2

I went through a period after my Norton virus program expired and I was without good protection. I then found my computer was hijacked by this virus:-

 

"Police Central e-crime Unit virus"

www.prlog.org/11795782-police-central-crime-unit-virus-how-to-remove-pceu-scam.html

 

 

 

I ran Avira Anti-Virus in safe mode and it managed to block some files associated with it and delete them, but I don't think it completely removed it. I then bought Norton Internet Security 2012 and found that it detected Trojan.ZeroAccess (as well as variants C and B) and Trojan.Gen.2.  I am wondering if the "Gen" trojan is part of the remnants of the Police e-crime virus that used to disrupt my system. Maybe it is still trying to disrupt it but Norton is blocking the attempt and informing me with occasional pop-up notices that trojans are being blocked. 

 

How do I remove these malicious programs? Norton keeps detecting them and telling me its blocked or removed them, but they keep coming back and so Norton has to block them constantly. This is not good for my system performance.