So... is Izumo: Takeki Tsurugi no Senki finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 19, 2005
Manga finished: June 10, 2006
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
Yagi Takeru, an orphan raised in the Touma household, enjoys a peaceful life surrounded by friends and rivals.
His ordinary existence is shattered when a sudden earthquake transports him and some of his classmates to a strange, desolate version of their school.
Finding their town eerily deserted, Takeru, along with Seri and Asuka, encounter mysterious cloaked figures.
They learn that they have been brought to an unfamiliar world, thrusting them into an unknown conflict and a journey for survival.