1. Lacking in harmony, compatibility, or appropriateness.
2. Inconsistent with reason, logic, or common sense.
I have since often observed, how incongruous and irrational the common Temper of Mankind is.
--Daniel Defoe, [?]Robinson Crusoe
She made nightdresses and petticoats in the old-fashioned mode and sold them to a shop in the market town -- one of those exclusive little shops with a single garment and something imaginatively incongruous -- a monkey's skull or an old boot -- arranged in the window.
--Alice Thomas Ellis, [?]Fairy Tale
They made an incongruous pair as they walked on: one was slight and dapper, some thirty-five years in age, with long, clipped mustaches, and dressed in the height of modern elegance, complete with pearl buttons and gold watch chain. The other, ambling a few paces behind, was a towering fellow with grizzled mutton-chop whiskers, whose ill-fitting frock coat barely contained a barrel chest.
--Ben Macintyre, [?]The Napoleon of Crime
Incongruous comes from Latin incongruus, from in-, "not" + congruus, "agreeing, fit, suitable," from congruere, "to run together, to come together, to meet."