Most will say "Use a food grade Mineral Oil to lube ..." (found in the laxative section of the grocer or pharmacy)
Over the 60 or 61 years I've carried a knife, I've used 3 in One, new and used 10W30, new and used ATF, oilve oil, WD-40, Hoppy's Gun Oil, bacon grease ...
Lube the joints, and wipe off the excess.
"Discoloration" ... are the blades CV/Carbon Steel or Tru Sharp/Stanless Steel?
If CV/Carbon steel the discoloration is patina. Patina is a good thing. It is non-toxic, and helps prevent the blade from rusting.
You can remove it with somethig like Never Dull, but it will return if you use the knife. Personally, I'd just leave it and let it develope and change over time.
The corrosion inside ... brass, Nickle Sliver, or steel liners?
Brass and nickle silver liners and bolsters can be cleaned with Real Lemon lemon juice (or lime juice, or catsup)
Note: if you soak the knife in lemon or lime juice and the blades are carbon steel, you will get a patina on the blades.
You could also open the blades and clean the inides with oily 0000 steel wool or a scotchbrite pad.
If there is more than one blade on a spring, open one fully then the other fully, to lessen the chance of breaking the backspring.