So... is Ore, Twintail ni Narimasu. finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: December 26, 2014
Manga finished: December 18, 2020
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Ore, Twintail ni Narimasu. is about Souji Mitsuka, a high school student with an intense passion for twintails.
His obsession takes an unexpected turn when aliens arrive on Earth with the goal of stealing everyone's "attribute power" and, oddly enough, twintails.
Souji is granted the power to transform into Tail Red, a warrior with twintails, and is tasked with protecting Earth from the invading alien force known as Ultimegil.
Alongside other twin-tailed warriors, Souji must learn to control his new abilities and fight to defend not only the planet but also the hairstyle he cherishes.