So... is Asobi ni Iku yo! finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 26, 2010
Manga finished: February 25, 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
Asobi ni Iku yo! centers around Kio, an ordinary guy whose life is turned upside down when he encounters Eris, a cat-eared alien from the planet Catian.
Eris has come to Earth to study humanity, and she decides to stay with Kio, bringing a lot of unexpected changes to his everyday life.
However, Kio soon realizes that Eris's presence has attracted unwanted attention. Various organizations, each with their own agenda, are determined to capture or eliminate her.
Kio finds himself thrust into a dangerous situation, forced to protect Eris from these secretive and powerful groups, even when those around him are not who they seem.
The series follows Kio's efforts to keep Eris safe while navigating the chaos and conspiracies that surround her, all while dealing with the... ahem... unique aspects of having an alien cat-girl living in his home.