So... is Senjou no Valkyria finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: September 27, 2009
Manga finished: September 01, 2011
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
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Synopsis
The anime Senjou no Valkyria tells the story of Gallia, a neutral nation invaded by the Europan Imperial Alliance for its valuable Ragnite resources.
Welkin Gunther, along with his sister Isara, is forced to take action when his hometown is attacked.
They join the local militia and eventually become part of Squad Seven, a unit tasked with defending Gallia from the Imperial forces.
Despite their inexperience with war, Squad Seven must fight to protect their homeland and face the challenges of a war they never expected.