[urgoroger]

It might be easier to view entropy of a state as sort of the probability that that state would occur after randomly arranging all of its parts (usually particles). In fact this is pretty close to the actual definition.

Here's an example: Suppose you had a container and you put some marbles at the bottom such that there are reasonably large gaps between the marbles. Now if you close and then shake the container hard (this is the 'random arrangement' process), then it is with high probability when you open the container that the marbles will be arranged reasonably spread out across the bottom. In this sense, when the marbles are spread kind of far apart in the container, it is in a state of high entropy (probability).

There is also the chance that when you open the container the marbles form a perfect straight line at the bottom. However, this is much more unlikely, so that you would consider this a low entropy state.

Now, consider the universe in place of the container, and subatomic particles as the marbles. Randomly configuring all of these particles, it would be really hard to end up with a stars, galaxies, humans. These are like straight lines in the marble example. It is much more likely you just get a soup of somewhat uniformally distributed particles (as in the marbles just being sort of randomly spread out from each other). This is what you describe as "a perfectly uniformly distributed of zero temperature mass (or maybe absoute zero, not sure) of grey energy is the perfect order". It wouldn't really be 'perfect' in some senses of the word though, which may be your cause of confusion. It would be more like if you took a snapshot of the static on an old TV.

[posterboy]

The common depiction is of a bunch of particles of two kinds, sorted into separate compartments by kind, which will mix if a divider is removed. In this picture, every part of one kind receiving a partner of the other kind, that can be called a state of order. If we take heat instead, every particle swinging differently is more chaotic--at least in my understanding--than all synching up so that their speeds relative to each other are zero ... 0 degree is just not higher order, because "high" is associated with high frequency (or energy or order).

In your shaky example, you transmit energy to the system by shaking, so if shaking a certain way, you'd well expect standing waves, if shaking a bit more you'd pulverize the marble and ultimately a hot plasma with density gradients. I wonder how hard you'd have to shake and swirl to eventually get a black hole, for which the notion of entropy doesn't even really make sense, if you aren't inside.