The act of being a douche; The act of being an asshole.
If someone where to throw you in a trashcan then laugh and leave, that'd be douchish. Or the best example of all, if someone were to not even acknowledge your presence because of the people they hang out with. (Or if you tried to break up a perfectly fine relationship for your own benfit, you'd be acting douchish.)
A spin-off of a douchebag; refers to a guy who is guilty of and/or has committed some form of douchebaggery. Doucheshnozzles really capture the essence of doucheness, and therefore are usually repeat offenders, i.e. they're douchey all the time, and may never grow or develop into normal, decent males.
A doucheshnozzle is a guy who stands in club lines for two hours in the hopes of rubbing up against some girl for four seconds. Guys who pose in pictures with pseudo hand gestures to act like they're cool, when in reality they are complete doucheshnozzles. Frat boys who drink crap-beer and attempt to bone women who are intoxicated or likely passed out.