So... is Katanagatari finished or not?
YES, it is finished.
Why?
The anime finished after the manga:
Anime finished: December 11, 2010
Manga finished: December 04, 2007
MangaUpdates contains information about the anime adaptation and indicates that it is complete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Katanagatari is set in an alternate Edo-era Japan where sword fighting is a prominent art form.
Shichika Yasuri, master of the unique "swordless" Kyotouryuu style, lives a secluded life with his sister.
Their quiet existence is disrupted by Togame, an ambitious strategist who needs Shichika's help.
Togame seeks to collect twelve legendary and powerful swords, known as the Deviant Blades, for the shogunate.
Shichika, intrigued by Togame, agrees to assist her on her dangerous quest.
Their journey is fraught with peril, as they must overcome skilled opponents and those who also desire the swords.
The story follows Shichika and Togame as they travel across the land, facing challenges and forming a strong bond while pursuing Togame's objective.