Annoying pop-ups? Please help?

((MAKE SURE YOU READ THE WHOLE STORY)) Ok, this is the background story. So yesterday I was doing some research for a project and I googled a website and as one of the results was a link(it was like #4 from the top) to it. I click the link and it took me to a COMPLETELY different site. I closed to internet window, started a virus scan(I have AVG free) and it came up with 3 viruses, (2 were trojan horses, and the other one was a file that made a reference to a corrupted registry or something like that). I came home today to get on my computer, and I tried and tried to open the internet, and it was unresponsive. I logged off, logged back on and a window comes up(titled "Resident Shield Alert" from AVG) and it said I had 6 more trojan horses. I told it to remove them and it said it sent them to the virus vault. So now, when I google things and it says it's a link to a respected website, it takes me to a random "shadowy" website sometimes, for instance I just googled "anti virus program" and the first link to was a website that said "toolbar.google.com" and it took me to a website that was nothing like google, second, when I get on to any website(youtube, facebook, google, etc.) it gives me random pop-ups that are all about random things (most of them are about a registry doctor and anti virus program, and/or have something to do with the website I'm on. I use firefox, and have the "Block Pop-Ups" option on. Currently, I'm downloading avast! as I am unhappy with AVG's performance. Now to the questions:

1)How the heck do I get rid of the pop-ups

2)Do you think my computer has a virus

3)If so what should I do

4)Are there any programs I should get that might be helpful(if not ignore #4)