For descriptive purposes, when a Strix is sitting it looks like a shadow owl, when it's attacking like a cloud of mist shadow, and smoke. What's it look like when it flys? does it retain an owl form (flap its wings)? or look more like the Smoke monster from Lost or the Demons in supernatural? but with glowing yellow eyes.
Blood and Smoke, p197:
When in motion, a Strix half-flies, half-flows... a Strix can lose all of its owl-shape entirely to flow through any crack.
Seems like the Strix has the option. In-character, I'd suspect it's whatever the Strix prefers, probably based on what will cause the most horror in observers.