KCW:
Are the inner and outer ones asymmetrical or something? They just don't look right.
They are both symmetrical, but also both rather complex. I think on those images you are only seeing a portion of the tartan, which is probably why they appear assymetrical to you.

AllenJ:
Is there any difference between the Strathspey tartan and the Black Watch?
Yes. But they are very similar in appearance, both being blue, black and green tartans. The difference can best be illustrated by comparing thread counts. (K = black, B = blue, G = green)

Strathspey:
K4 B4 K4 B20 K20 G20 K4

Black Watch:
B22 K2 B2 K2 B2 K16 G16 K2 G16 K16 B16 K2 B2

In essence, the Black Watch has two and four black lines alternating on every other blue feild, while the Strathspey has three black lines on every blue field.

The Black Watch is the same as the Sutherland tartan, on the other hand.

Frank:
Has there been any official adoption of the South Uist tartan?
There are actually three tartans that I am aware of recorded as "South Uist," all of which are artifact tartans (two of which I know of date from the 1730s, the other one I am not sure of the date). So that haven't been officially adopted by the island as true district tartans, per se, but they are historic tartans from the region and if someone wanted to wear a tartan to identify with the island, one of these historic designs would be a good choice.