Hmm, his greed feels like the most obvious choice. He's obsessed with gold, money and treasure, and that's a key trait in every game and series he's appeared in.
His strength and brutishness is up there, though moreso in Wario Land than WarioWare. Weirdness is there too, but that's mainly about his world/series rather than him in particular.
The biggest thing that sets Wario apart from Mario even more than his more thuggish traits, is that Mario is very reactive. His stories are driven by wanting to help others in any given situation.
Wario meanwhile is entirely driven by his own desires, which can one way or another, always be drawn back to greed. Wario wants something, he takes initiative to get it.
Shake It in particular does a wonderful job portraying that. He could care less about the captured princess or terrorized world he's being told about, but the moment a possible reward that satisfies his greed is on the table, he's right on it, with all the good he does in the process being entirely incidental.
I always preferred when Wario is portrayed as stronger and more brutish, and yet greedy at the same time, if I said my thoughts it would just repeat what has been said. Wario Land games always felt best to me whenever it felt like a seperate game. Wario goes into different realms often, the mystery and the lore intrigue me. Wario's need for gold and power is also something I love. he's a perfect charater.
I think his greed would be my answer as it is the reason we see all of his other traits, but another one I quite like is his stubbornness. When it comes to Mario platformers, I refuse to believe the concept of 1-Ups is canon, seeing them purely as a functional purpose for how the player can keep playing. Therefore I see Mario as more of a "first try" kind of hero, able to breeze through any challenge thrown his way in canon. Wario being so desire-driven gives him a "if at first you don't succeed" flair when it comes to losing challenges, particularly in WLII and 3 where control is almost never taken away during the player. It feels canonized that Wario trips up and fails, only to get back to his feet and try, try again, which has both humorous and admirable results.
I'd say Wario's most defining trait is his greed without a doubt, but sometimes his brutish nature too. The first paragraph of his Wikipedia page defines him as "a selfish and greedy treasure hunter". (Wario - Wikipedia)