Just some simple metal polish, like Flitz, Simichrome, etc, can remove that verdigris. Doesn't take much work to scrub it off, with the polish.
As mentioned, vinegar isn't really the best option for cleaning knives; especially if it's left to sit on the metal too long. The brass, nickel and steel are all reactive to the acetic acid, and that'll generate corrosion like the verdigris seen in your pics (it's the copper, in the brass alloy, reacting to the acid). This is the same sort of reaction seen with knives stored long-term in leather sheaths; the leather often has residual acids left in it from the tanning process.
David