If an opponent plays Valar Morghulis and I play Outwit but I have no characters with the learned crest but I have character abilities or event cards that can give a character the learned crest do I still have the time to play those abilities?

For example lets say I have the character card Jack of All Trades. During any phase he can kneel 1 influence to give himself the crest lerned for the rest of the phase. Could I do this to fufill the criteria for Outwit?

Not after the plots are revealed. Once plots are revealed, there is no window in which to trigger anything until all plots are resolved. You'd have to use the effects to give a character the Learned Crest BEFORE plots are revealed - potentially tipping off your opponent that Outwit is coming, but them's the breaks.