So... is Asu no Yoichi! finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 27, 2009
Manga finished: February 05, 2011
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Asu no Yoichi! tells the story of Yoichi, a young swordsman raised in the mountains, who's sent to live with a family of sisters in the city.
His mission is to learn more about the modern world and improve his swordsmanship, but he's completely unfamiliar with contemporary society.
Yoichi's old-fashioned behavior and lack of social skills lead to many humorous situations as he tries to adapt to his new life with the Ikaruga sisters.
The anime follows Yoichi's struggles and comical misunderstandings as he attempts to navigate the complexities of city life and build relationships with those around him.