I've found cleaning the SA shifters is ez, if the shifter itself isn't a total write off, you need to unhook the cable so that you can freely access with a small cleaning tool.. yes you can still order SA cables, hell you can order a new SA shifter if your inclined. Sorry haven't delved far into wheelbuilding, you'll need someone else for that info.
Classic shifter here
http://www.amazon.com/Sturmey-Archer...7061571&sr=8-1
Here's the cable with the two differerent tensioners
http://www.amazon.com/Sturmey-Archer..._bxgy_sg_img_b