What is the angle between the planes of Oumuamua's hyperbola and the Milky Way Galaxy? Viewing the animations of Oumuamua passing through the solar system, it is apparent that the plane of its hyperbola departs from the plane of the ecliptic by a large amount.  The plane of the ecliptic departs from that of the Milky Way Galaxy by a large amount.  Now that there is so much speculation about a potential artificial origin, one might be forgiven for speculating that there might be a coincidence between the Milky Way Galaxy's plane and that of Oumuama.

What is the angle between the planes of Oumuamua's hyperbola and the Milky Way Galaxy?
The inclination of the orbit is 122.7 degrees (with respect to the ecliptic), whilst the Galactic plane is inclined at 60 degrees to the ecliptic. So there is 63 degrees between the two.

Such a high inclination by no means rules out that the object is orbiting within the Galactic disk. A study by Mamajek (2017) concluded that it's approach trajectory was entirely consistent with an object travelling at the median velocity of stars around us. It had insignificant vertical or radial motion with respect to the local standard of rest, but is travelling about 10 km/s too slowly for a circular orbit at the Sun's Galactocentric radius (whereas the Sun moves about 10 km/s too fast).

This appears to be discrepant with the inclination angles discussed above until you recall that the sun is moving up and out of the Galactic plane at around 7 km/s.

Have a look at the animation at https://www.cosmos.esa.int/web/gaia/iow_20180925 , it says a thousand words. It shows time running backwards from the time of encounter and shows how Oumuamua comes in from inside the Sun's Galactic orbit and from "above", with respect to the Galactic plane.