In experience with CRT type TVs & monitors, I've had to repair some badly charred PCBs.
To clean pcb legs, try a pencil eraser. There is fine abrasive in them. Try to use the white eraser with silica - the red/pink have some amount of iron oxide that may cause trouble with soldering if any dust is left behind. Be sure to support the leg flat against the workbench then polish the inside edge of the leg. Find something to support the inside edge before polishing the outside edge (be extremely careful not to bend the pins).
Your best bet is immersion in an ultrasonic cleaner with water & detergent, or the kitchen sink and a stiff brush - make sure there's no corrosion debris bridging pins, or any pins eaten through. Then dry it thoroughly. You can get various spray on conformal coatings that should prevent any further corrosion.
The fine grit in the pencil eraser allows the pencil eraser to polish the metal. You can also try a more aggressive polishing grit or even scraping with a razor blade, Exacto knife, or even a file. Be careful with a file, the metal pins are very soft and will likely clog the file immediately.
Something else to try is a solution of warm water and baking soda. Cut the bristles of an acid brush down on an angle and use it to scrub the pins and around the ICs. Once the heavy stuff is dissolved then rinse with clean water and finally isopropanol alcohol. Dental pics can also help in dislodging chunks of corrosion. Combine that with GopherT's suggestion and you should be able to remove most surface corrosion and rust.
