On 1 March 1939 Oesau joined the Headquarters Flight ("Stabsschwarm") of I./JG 2. By 15 July 1939 Oesau was promoted to "Oberleutnant" and given command of 2./JG 20. On 15 July 1939, I./JG 20 was activated in Döberitz initially consisting of two "Staffeln" drawn from JG 2. Prior to the invasion of Poland I./JG 20 was transferred to Strausberg on 26 August 1939. From there, the group was transferred to Sprottau (modern Szprotawa) anticipating an attack from the Polish Air Force. A week later the group moved to Brandenburg. On 21 February 1940, the unit was relocated to Bönninghardt under the control of JG 51. It continued to operate in this fashion until the end of the Battle of France. On 4 July it was re–designated III./JG 51. Oesau served as "Staffelkapitän" of 7./JG 51.