I was playing a game recently and it came down to a challenge where I was attacking with 2 characters who both had deadly and the defender was blocking with a character who had renown. I would have lost the challenge but if deadly was to take effect before renown, then I would have won the game, but if the defending character claimed renown first then she would have won the game. Which one takes effect first?

The "Resolve challenge" framework action window goes like this:

1. Determine winner
2. Implement claim
3. Award Renown
4. Award unopposed
5. Passives (including Deadly)
6. Responses (except saves and cancels)
7. Remove moribund cards from play

So Renown always happens before Deadly. But even if Deadly happened first, the character would be moribund until after all responses have been resolved and power on moribund characters counts for victory like power on any non-moribund character (the power is discarded when the character effectively leaves play at the end of the action window).

3 and 4 are backwards. Awarding power for "unopposed" comes before awarding power for Renown.

I stand corrected.