There are a few websites listing German military casualties.
The organization that has the most detailed information about German WWII soldiers is "Volksbund Kriegsgräberfürsorge". Not all individuals they have on file are in their database yet, it's worth to contact them even if you don't find the soldier listed in the database.
Geogen, which stands for Geographic Genealogy, is a project created and maintained by Christoph Stoeppel. Based on telephone book entries he created a mapping tool for family names in Germany (in its present-day borders). While it might not be useful for very common family names, such as Schmidt, Müller, or Schulze, it can be helpful with rather seldom family names. If one of those family names is especially heavy concentrated in one county, the immigrant ancestors might origin in this county.
There are two great sources available for outlining German genealogical research.
The first is very detailed but older (last updated in 2004) and published as a PDF. The second source is shorter but contains many links, accessible on FamilySearch Wiki.
The Hamburg Passenger Lists were created when passenger ships left the Hamburg harbor. Depending on the year, they contain different levels of detail about the individual passengers.
Covering Niedersachsen (Lower Saxony, called Hannover), Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
Covering Niedersachsen (Lower Saxony, called Hannover), Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
Covering Niedersachsen (Lower Saxony, called "Hannover") Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany.
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
Covering Niedersachsen (Lower Saxony, called Hannover), Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany.
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
Covering Niedersachsen (Lower Saxony, called Hannover), Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
Covering Niedersachsen (Lower Saxony, called Hannover), Braunschweig (Brunswick), Schamburg-Lippe and Oldenburg from Volume X of the Atlantic Bridge to Germany.
The Atlantic Bridge to Germany, Volume X was published in 1999 by Mondo Genealoga Ligo, Salt Lake City, Utah
By Charles M. Hall and Alice Woods Schiesswohl of Salt Lake City
