"Der Sang", "der Gesang", and "der Song" all mean "a song". What are the differences, if any?
Song vs. Lied
One word is missing from the list, namely Lied. A Lied is a piece of music which is supposed to be sung, a song. For certain types of songs the word Song taken from English can be used instead of Lied, however while you might speak of a Beatles-Song you would not speak of a Schumann-Song.
The word Gesang denotes singing.
Ich lauschte ihrem Gesang.
means that I listened to someone singing, it does not imply that the song she sang was hers.
Sang is a variant of Gesang which is mostly obsolete, but preserved in certain expressions (mit Sang und Klang, sang- und klanglos). It also occurs in the second stanza of the Deutschlandlied (note -lied):
Deutsche Frauen, deutsche Treue,
Deutscher Wein und deutscher Sang
Sollen in der Welt behalten
Ihren alten schönen Klang,
Uns zu edler Tat begeistern
Unser ganzes Leben lang.
Now, that is a form of patriotism that I can live with, even though its sexual politics are a bit outdated.