"Oily" sounds like it has been used show how the writer feels this smugness is unpleasant, I couldn't say exactly how, but I think it is supposed to create an image. Perhaps, compared to being "brash", this is equally unpleasant but in the way that an unwanted guy trying to talk to a woman at a bar is. So where "brash" is very obvious and loud, "oily" is more subtle. I'm getting an image of a snake, slithering around. Still unpleasant, but not as obvious as a bear stomping around the place! Hope this helps!

Hi Sasha, One who exhibits "brash arrogance" is bold in an offensive manner and treats others condescendingly through words or actions. We can imagine "oil" as a lubricant, and reduces friction. As an analogy, a person of "oily" character tends to flatter and win others over to his or her cause. So a person who claims something with "oily smugness" does so with self-satisfaction and sugar-coated words, aimed at gathering approval and support. Obviously, a person who can switch between brash arrogance and oily smugness when handling foreign affairs can be self-contradictory, self-defeating and unpredictable. The former offends others by exuding an air of superiority while the latter annoys others with a weakly veiled pretense and insincerity. Hope this helps.