I'm really interested in learning about Imperial Japan and the like. Is most of the information outdated by the time you get to SR4, or is it still good for setting and stuff?

Well, when they wrote the later sourcebooks, they knew SR4 was coming out, so they made sure they'd still be relevant after SR4.

That being said, I found there were gaps, especially technology wise. For the cultural aspect, no problem. But when, especially for Japan, there is a large section devoted to the new SOTA Matrix system being implemented or whatever, well, you can rip those pages right out of your book. But you still get a very good feel of things, and plot hooks, although 5 years old by SR4 standard, are still good ideas you can update to SR4. Who's gonna know?

Do they have lots of info about Asia in SR4, so much that I won't need Shadows of Asia, or does Shadows of Asia have a lot of useful information itself?

I would definitely suggest buying Shadows of Asia. SR4 has to cram an entire world's worth of history into one chapter. SoA and SoE both spend chapters laying out the explicit history of an individual country's growth and advancement towards 2065.

Runner Havens will provide an in-depth look at Tokyo in 2070, but for the rest of Asia and Japan, Shadows of Asia is going to be your best source at least for a few years until the FanPro team updates the material.

You should definitely pick it up. It's a little heavy on fluff unlike the meaty Shadows of Europe book and at times a bit stereotypical in their "coverage' of some places, but some of the writing is damn good, and there are a lot of great Shadow Run ideas in that book. China itself is great because you have so many different flavored balkanized countries pretty close together. I think it really opens up a lot of possibilities to the types of runs you can send your players on and still keep them somewhat local. Plus, its not Seattle.