Touji :

It is not easy to classify Touji according to the Systema Sephirotica, but the best fit would be Gevurah.
Gevurah's vision is power, it's illusion invincibility, which fit's to Touji, because he tries to solve his problems by force and thinks of himself that he will always manage his problems.
His vice would then be cruelty, which explains why he has to kick Shinji in the butt when he realizes that Shinji piloted the EVA that injured Touji's sister.
When they finally become friends, Touji insists that Shinji should punch him in the face so they were even, which relates to Gevurah's qlippah, Bureaucracy.