Well i haven't used Adaware in a while but i remember that you shouldnt really outright delete each of the 'infections'. There is a quarantine facility that will just remove the offending files to an archive. Then after rebooting your PC you can be sure that any changes that were made were not threating your system. Then you can delete the quarantined files.
Also make sure you have a firwall up, and make sure only KNOW processes are allowed to contact the internet. Then again run Adaware. This i rememeber stopped re-infection. I also suggest that you use SpyBot Search & Destroy, it will get rid of alot of spyware on your system and it can patch certain vunrabilities on yout system.
p.s. You might wanna try to use the Windows update - im assuming that your using Windows, dont think that Adaware has another OS client - facility to get your Windows patched with all the latest security. But you might not wanna do that, i certainly didnt, my system breaks with SP2 for WinXP