Does the axis of the solar system line up with the Milky Way, or is it more generally perpendicular?

we are on the outskirts of one arm of a spiral galaxy we call milky way. imagine a wheel with the axle, we are on one of the spokes

you can also see http://casswww.ucsd.edu/archive/public/tutorial/MW.html

It’s askew by about 60 degrees.

The plane of Earth’s orbit around the sun is called the ecliptic. The galactic plane is, well, you guessed it. They intersect at an angle of about 60 degrees.

If you are away from city lights you will be able to see the milky way going north\south at night, so its like a wheel on a wagon

Over time, it seems like gravity would pull everything in the galaxy into the same plane.