What is linear momentum? Is it as the name implies? Is everything in the universe thought to be moving all on one plane? This sounds incredibly limiting. The universe's mass should be moving in ALL directions, outward, upward, downward, etc. I believe matter to move about the universe following the path of least resistance, much like water on earth.

Here is the best explanation of linear momentum that I could find.

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Linear Momentum

Nice link from MkStfnz. The universe's mass DOES move in all 3 dimensions and is spread out in all directions throughout space. There is some large-scale structure but it's foamy in 3 dimensions.

The overall expansion of the universe appears to be isotropic, that is, the same in every 3-dimensional direction.

Matter of course "moves about" under the influence of forces, especially gravity, as described by Newton's laws and general relativity. The flowing water analogy doesn't seem to fit very well with space science, but "following the path of least resistance" is a more-or-less universal tendency of physical systems, which I think is what you meant.

Our Milky Way galaxy, like most galaxies throughout the universe, is flattened like a pancake but thicker in the middle. This is due to rotation, which gives it angular momentum in addition to linear momentum. But if you look at many different flat galaxies, they are oriented at random angles to one another throughout space, so there is still no preferred plane or direction overall -- just locally.

Likewise our solar system -- the sun and planets -- is more or less confined to a plane because of its rotational angular momentum (which was already present in the dust and gases that it formed from). But if you look at planets orbiting other stars -- now actually possible! -- they are in random orientations relative to our own solar system.