So... is Mushi-Uta finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: October 05, 2007
Manga finished: April 26, 2014
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.
The mangas and the non-core contents are excluded by default, but you can enable them by clicking the buttons below:
Synopsis
In the near future, bizarre insect-like beings called Mushi appear, granting supernatural abilities in exchange for people's dreams. These people, known as Mushitsuki, are a source of both wonder and fear.
Daisuke "Kakkou" Kusuriya's life is changed when he meets Shiika Anmoto, a seemingly innocent girl.
Unbeknownst to Kakkou, Shiika is an escapee from GARDEN, a secret prison holding Mushitsuki.
GARDEN, under the Special Environmental Conservation Executive Office, sends a powerful agent to recapture Shiika.
However, they are met with opposition from the Mushibane, a resistance group led by the enigmatic "Ladybird," who seek to protect Mushitsuki from GARDEN's control.
Kakkou finds himself caught in the middle of this conflict, his connection to Shiika drawing him deeper into a world of secrets and dangerous powers.