Not odd at all, really. It's only relatively recently in human history that we've discovered that stars are just faraway suns. Prior to that, it was believed that they were totally different types of celestial objects. A fantasy universe like this one can go with whichever interpretation it likes.
However, it IS stated that Midgardsormr carried his brood to Hydaelyn from another star, I believe, which implies that it is known in the game that the sun is also a star... Or perhaps, the planet is. In this cosmology, it could easily be the case that the sun is not a humongous ball of nuclear gas, but instead a small, but very warm object also in orbit around Hydaelyn. (Think of how the sun is portrayed in the Discworld series of books.) So, the stars we see in the sky are other planets like Hydaelyn, visible because they also have tiny bright suns spinning around them.
Even in the tiny sun case, though, your question is still unanswered: Why couldn't AST get more star power from the sun, an incredibly nearby star? There's a couple of explanations. Perhaps they DO - but star power does not dilute over distance. The amount of energy we get from our sun is no greater or lesser than we get from far suns. The sun is just another celestial body providing exactly one celestial body's worth of Astrologian power. Or, another explanation, perhaps traveling interstellar distances cures or tempers the star power in some way that makes it usable to Astrologians, while the nearby sun's power doesn't travel long enough to get the same effect. The space between astral bodies has, after all, been referred to as "the aether" in classical times in real life; perhaps there's some kind of aether star power travels through as it moves that empowers it in some way.
There are many possible explanations - and the game itself hints at pretty much none of them. Probably never will, either, as delving into this kind of nitty-gritty is a great way to get your lore tangled up over time. :P