I don't know very much about viruses; I went to a website recently and aVast blocked a few trojans that tried to enter my computer. I ran virus scans with aVast!, Spybot, and Ad-Aware 2007 and no viruses were found. How likely is it that if a virus somehow managed to initially get past my anti-virus programs, it could further avoid detection by all three virus scanners? Also, if there was a virus on my computer, would it always show up under the running processes listed in Task Manager?

Ah your fine its nothing to worry about i always run into site's like that and i love the Avast its great.

I would say it could be very likely all three could show clean but you could still have something on there. AdAware especially is not the program it used to be. Avast and Spybot both are very good programs but there ARE certain Trojans which are not picked up by those two.
No, if there IS a virus or Trojan on the computer it will not always show in the task manager, it would have to be running at the time to show in the task manager. There are some that only run at start up and then shut down. There are others that would only run when specific programs are used and if you don't happen to be using those programs at the time then the infection would not be running and wouldn't show in the task manager. There are some which place themselves into your task scheduler and only run at specified times in order to download more infected files.
You all ready have run two programs which show nothing and that it great, but since Avast did warn you then you know that you were "under attack", to be very safe then I would suggest the following:
download Malwarebytes' Anti-Malware (MBA-M) to your Desktop.

* DoubleClick mbam-setup.exe and follow the prompts to install MBA-M.
* Be sure a checkmark is placed next to Update Malwarebytes' Anti-Malware and Launch Malwarebytes' Anti-Malware, then click Finish.
* If an update is found, it will download and install the latest version.
* Once the program has loaded, select Perform full scan, then click Scan.
* When the scan is complete, click OK, then Show Results to view the results.
* Be sure that everything is checked, and click Remove Selected.
* When MBA-M finishes, Notepad will open with the log. Please save it where you can find it easily. The log can also be opened by going to Start > All Programs > Malwarebytes' Anti-Malware > Logs > log-date.txt.
Reboot the computer

Download and run a Full System Scan with HiJackThis. Save the log and post back here with the MBA-M log and the HiJackThis log.
It is better to be safe than sorry.

To cut a long post short. The answer to your question is Yes a 'virus' as you say can hide from all three scans. And No!Task manager does not pick up ALL process. Remeber theres a BIG difference between viruses, trojans, and spyware, adware. Anyways im not explaining all that. I would recomend to you to get a copy of Kaspersky with up to date signitures. I would further recomend a rootkit scanner. Rootkits are programs that are able to hide sometimes even from the best of AV. I would also recomend an advance task manager to view all running processes

No need for another av program, Avast is excellent.

JHolland1964, I did everything you said, I attached the two log files; can you determine if I have any more trojans / viruses from the log files? I guess it's hard to determine what the trojans on my computer have been doing this whole time; for all I know, somebody has my credit card number and passwords if they were key loggers (right?).

Is Process Explorer by Sysinternals a good advanced task manager (that's what I have now) ? I had trouble following everything on it so I just use the regular task manager.

Your logs look good. Doesn't appear to me that you had anything which would be a password stealer on there. You don't appear to be running a firewall, unless you are running the Windows Firewall.
Now your infections were from downloaded programs...torrent downloads.
One way to avoid this of course is NOT do it. But if you must then one thing you must do is SCAN every downloaded file with your AV program AND MBA-M BEFORE opening.
Another prevention measure is to use the program SpywareBlaster. It is really a MUST have. Download, install, update and enable all. Close the program, that's it. Just check manually for updates weekly.

Okay, thanks jholland, you've been really helpful I appreciate it. Just out of curiosity, how can you tell the trojans weren't keyloggers without looking at the source code of them?

I just go through the names given. There are many places online which will give you the particulars of these trojans, what they do, where they come from, etc. Most of the reputable av sites will give this info if you have the file name. Remember, all this has to be known before there can be a good remover developed.

Aside from being free, are there advantages to SpywareBlaster over the Protection Module in Malwarebytes' Anti-Malware (which you have to pay the registration fee in order to get)?

Ken