Will the avast system take the duties of the “ad-aware” or should i continue using it?

No, avast is not an antispyware application, only an antivirus.
You need to keep not only Ad-aware but you can take a look into SpyBot and into SpywareBlaster :wink:

I agree with Technical. You may also have a look at the malware removal section and the HijackThis section on my website to gather more information. Click on the link in my signature to get there.