So... is Arad Senki: Slap Up Party finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 26, 2009
Manga finished: September 30, 2009
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
Arad Senki: Slap Up Party tells the story of Baron, a man living in a land touched by a mysterious and corrupting energy known as the "cursed light of Kazan."
This curse has afflicted Baron, possessing one of his arms.
He discovers a sword inhabited by a spirit named Roxy, and together, they set out on a journey.
Baron's quest is to uncover the truth behind the curse plaguing the continent of Arad.
Along the way, he encounters various individuals who join him, forming a party to aid him in his challenging endeavor.