Shtick has long been mainstream English in the United States and is now making its way into British use. In colloquial parlance, it means, roughly, personal, idiosyncratic or trademark behaviour with which someone is particularly associated.
You might say that wearing kabbalistic symbols is today part of Madonnas shtick, or that having a gentleman in a crimson jacket with a booming voice make the announcements at wedding receptions is part of Anglo-Jewish shtick. If you think that someones behaviour is idiosyncratic to the point of self-indulgence, you could call it shticky.
Shtick is Yiddish, defined in my dictionary as piece, pranks, whims or capricious carrying on. It derives from the German st