Warning: probably TLDR
This is something I've always been really curious about, because so much of Azumanga feels like Alice in Wonderland.
The most notable thing is that Osaka is EXTREMELY similar to Alice. Because her inner monologues aren't inside the movie, it's harder to realize but in the books, Alice has a mind that wanders in really odd ways. Here's some excerpts that seem very similar to how Osaka would act.
(after alice eats the cake to grow big)
"'Curiouser and curiouser!' cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English); 'now I'm opening out like the largest telescope that ever was! Good-bye, feet!' (for when she looked down at her feet, they seemed to be almost out of sight, they were getting so far off). 'Oh, my poor little feet, I wonder who will put on your shoes and stockings for you now, dears? I'm sure I shan't be able! I shall be a great deal too far off to trouble myself about you: you must manage the best way you can;—but I must be kind to them,' thought Alice, 'or perhaps they won't walk the way I want to go! Let me see: I'll give them a new pair of boots every Christmas.'