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.