The series title has no particular significance to the story. “Azumanga” is a portmanteau of the author’s name “Azuma” and “manga”, while “Daioh” comes from the magazine in which it was originally published, Dengeki Daioh. In the anime, “daioh” is mentioned during the next episode previews, used in context with the meaning “great king”.
Daioh or 「大王」 means great King in Japanese from what I recall
I haven’t learned the vocabulary for the first half of the title so I don’t know what that means yet
It’s a word in Portuguese. (Azinhaga)
The Japanese title looks like it’s wordplay