A "Trojan Horse" is usually used to refer to a type of computer virus rather than an actual instance of a virus. It's something that tricks you into running/installing it by pretending to be something useful and beneficial.
What exactly did/does AVG have to say? Did it offer you an option to delete it?
The fix is usually to delete or uninstall the Trojan, they're often not like other viruses that might infect other files that would then require cleaning.
Are you still updating Norton? A virus checker is really only as good as it’s last update, which is why it’s so important to update them regularly.
You really should only need one anti-virus tool, so if you're updating AVG then it's probably best to get rid of Norton.
I'm a big fan of a free tool called Ad-Aware that can scour your computer looking for malicious software, I've recommended it on here several times. You can download it here: http://www.lavasoft.com/products/adawarefree.php
I'd recommend getting it and running it on your machine to see what's there....
It depends on the trojan - some are relatively harmless, others do more damage. You can search the Norton site for more info, or other Anti virus sites, like Sophos often have a threat database you can search.