So... is Nobunagun finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: March 30, 2014
Manga finished: August 28, 2015
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
Nobunagun centers on Shio Ogura, an ordinary high school student caught in extraordinary circumstances during a school trip to Taiwan.
When monstrous creatures attack, a secret government agency, DOGOO, emerges to combat them using individuals with special abilities known as E-Gene Holders.
These E-Gene Holders wield weapons powered by the spirits of historical figures.
Shio unexpectedly discovers that she too is an E-Gene Holder, inheriting the power of Oda Nobunaga, and must learn to control her newfound abilities to protect herself and others.