The German occupation of Norway began with the invasion on April 9, 1940, and lasted to the end of the war in May, 1945. The size of the occupation force was immense--upward of 300,000 troops, or the equivalent of about 20 army divisions, enough for one soldier for every seven to eight Norwegian citizens.
The tune the German army is shown playing repeatedly, "We're Sailing Against England," was a Nazi "approved war song" for German soldiers in WWII according to the June 10, 1944, issue of Time magazine. It was composed by Herms Niel (1888-1954) and had lyrics by poet Hermann Löns (1866-1914), who was killed in WWI. Originally a German Navy song from WWI, it became popular during WWII.
The novel by John Steinbeck on which this movie is based never names the invaders (explicitly shown in the movie as the German Nazi army).
Natalie Wood appears in this movie as the little girl asked for her name by a German soldier, while in the line to buy some food. From 44' 32", she is clearly recognizable.