Osaka, while considered weird, isn't socially maladjusted. She's able to carry on conversations, weird as they are, without shouting, or mumbling, or looking at the ground. She looks into eyes. She makes facial contact.
She also shows a great deal of empathy, which is lacking in those with Aspergers. For instance, when Sakaki tries to choke back a giggle thinking of Chiyo's dad as Santa Claus, Osaka puts her hand on her (something those with Asperger's are loathe to do) and tries to make sure she's okay. Also, when Tomo was about to drop Chiyo into the ocean, Osaka rushes to the (ill-attempted) rescue, screaming in fear.
Osaka is weird, and some of her weirdness may be similar to Asperger's, but I can't see her having it. I think OP is trying too hard to identify with a beloved character, to the point of projection.
NTTAWWT...