>What would happen if an object was massive enough to exhibit gravity, but was not spherical or disc-like, akin to the natural heavenly shapes?

Say there was a huge cuboid, like a cosmic sheet of paper, massive cylinders and pyramids, or more complex shapes like post-modern "art" (Or a space highway?).
Also let's wave our wand and say these things are sturdy enough to not collapse in on themselves.
>What would the orbits of those things look like?