Omer Bartov's Wehrmacht work is quite good at looking at the Wehrmacht's criminality from a sociological or anthropological perspective. Hitler's Army and The Barbarisation of Warfare are good companions for each other, and explain the "why" of the massive complicity in war crimes.

Richard Evans' Third Reich trilogy (The Coming of the Third Reich, The Third Reich in Power, and The Third Reich at War) is also a good foundation for understanding Nazi Germany as a whole; The Third Reich at War specifically covers German war crimes fairly well.

Stephen Fritz's Ostkrieg: Hitler's War of Extermination in the East I have unfortunately not yet read, but it comes well recommended from our resident expert on Nazism, war crimes in the Second World War, and Shoah/the Holocaust, /u/CommieSpaceInvader.