Olenna's Cunning let's you search your deck for among other things an event card (unless that is the card type your opponent mentions). If you search for an event that has a response to winning a challenge is there anything in the new timing that would prevent me from playing that event card as a response right away to the same challenge that triggered Olenna's Cunning in the first place?

The basic answer is, "No, nothing is stopping you. If Reaction #1 to Triggering Condition X puts an event with Reaction #2 to the same triggering condition into your hand, you can use it in the same reaction window." So if you use Olenna's Cunning to search for an event with a reaction to the same triggering condition (like, say, a second copy of Olenna's Cunning), you could play it in the same reaction window for winning that same challenge.

The really technical answer, though, gets into the meaning of "right away." Since reaction windows nest in 2.0, you would actually have to give everyone the opportunity to react to you playing/resolving Olenna's Cunning (e.g., reactions to playing the event, searching your deck, etc.) before going back and finishing up reactions to winning/losing the challenge. So if "right away" means "your next opportunity to react to winning/losing the challenge," the technical answer is yes, you can play the "new" event. But if "right away" means "your next opportunity to play an event," the technical answer is no; you have to close out the nested reaction windows before going back to reactions to the original TC.