The Oort Cloud is continuous and its density falls off with distance, so it can’t be said to be at a specific distance. However there are estimates of an outer edge which place it around and occasionally beyond the Sun’s sphere of influence.

The Sun’s gravity is spherically symmetric, so it itself doesn’t exert any force to keep objects in a plane. Self-interaction of objects in the disk provides this force, through collisions or gravity. What the Sun does do is draw objects in, so the density of objects is greater nearer to the Sun, meaning there’s more self-interaction in the disk in these regions. The Oort cloud, though it likely formed in the disk, is far from the Sun and therefore underdense, so when orbits in the Hills cloud are perturbed and moved into the Oort cloud, there’s not enough self interaction to correct their inclination.

So, to answer your question: kinda, but maybe not in the way I interpreted your question to imply.