When it comes to sorting out iffy internal wiring, I always try to point people towards this,
http://www.wppltd.demon.co.uk/WPP/Wiring/UK_telephon...
Which shows how it should be done. These days it's fairly normal practice to connect only pins 2 and 5, and leave the others disconnected.
Take each socket off the wall, and figure out what is connected to what, and which colours are used to do it. Others above have gone through what tools you need, bear in mind you can buy a throw-away IDC\Krone tool for a £1 or so from your local DIY shed. They don't last, but will do a better job than a screwdriver.
If you can lilve with the router being at the master socket, just a bit tidier, buy a filtered faceplate and replace the existing "detachable" part. This will isolate all your internal wiring from the ADSL signal, and give results the same as using the test socket. You then don't need individual filters on the extension sockets.