It really depends on the context and intonation. However, if you check a corpus of current English, or just listen to people enough, you'll find that no one says "So so." in response to "How are you?". It's not in common use anymore. It would be an acceptable answer, sure. It just wouldn't occur to a lot of native speakers of English, and so it shouldn't be the only possible answer here.
Couldn't agree more. I think there's a usage difference between North American English and the rest of the world, but in the U.S./Canada answering "I'm okay" would very seldom be read as "good". "I'm good" would also fall pretty far short of its literal meaning, especially in informal situations.
I would consider alright a little short of positive myself, I think, but still more positive than so-so. I'd probably say alright is often close to "can't complain, but nothing to write home about" (though sometimes it could be enough to smile about) while so-so is more like "could be better, but not worth getting upset about"...
I don't think I've ever heard any of my fellow Americans say "so-so". I've almost exclusively encountered it when an equivalent term from another language is being translated /into/ English. "Okay" literally means "okay", but functionally = "so-so" as far as American English goes. If you answer "I'm okay" when someone asks you how you are, I'd say there's a reasonable chance that friends and family would follow up with "Just okay?"