the art of pulling strange faces

Alternative form of ドヤ顔.

(beauty) small face

(Buddhism) the nose and the faculty of smelling, one of the 五根 (gokon, “five indriyia”) or 六根 (rokkon, “six indriya”) / (anatomy) the root of the nose; the nasal root

coati

(slang) facial (sex act)

smug/satisfied/triumphant/proud face/look

(informal) a small nose, a pug nose / (informal) a flat face, a face with a small nose

posed look

an arrogant, proud first person personal pronoun; I, me, myself.