So... is Asagiri no Miko finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: December 26, 2002
Manga finished: June 30, 2007
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
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
Tadahiro Amatsu, a young man with uniquely colored eyes, finds himself hunted by a mysterious sorcerer and his demonic forces.
To defend the town from these supernatural threats, a young priestess-in-training named Yuzu Hieda gathers a group of high school girls, including herself.
Under the guidance of Yuzu's older sister, these five girls must train and learn to harness their latent abilities as priestesses to stand against the encroaching darkness and protect their home.