Once the Axis had conquered most of Europe including Greece and Crete, and in North Africa was approaching the Suez Canal, Nazi eyes turned towards the oil fields in Iraq and Iran. With control of the Levant, the Nazis could attack the Canal from both sides, and up into Russia to capture the Caspian Sea oil fields.
The Vichy French refused to give the British or Free French access to Iraq, and they would fight to keep it. Here it gets very confusing, on the Axis side is the Vichy French, Luftwaffe planes and ground crews, local tribes that were working as mercenaries for the Germans, members of the Vichy Foreign Legion and the Royal Iraqi Army. On the side side with the British were a small contingent of the British Army (from Transjordan), the Arab Legion, the Free French, anti-Vichy Iraqis, what was call the Levies (who were local conscripts) and Indian Troops.
The one important point on the side of the Axis was their air force and tank corps. The British had few planes (many were Bi-Planes), little artillery and no armor. People changed sides constantly or just disappeared into the surrounding areas taking their weapons with them. The ingenuity that the British used, and the use of the Bedouin irregulars, allowed the British to force out the Axis troops and preserve the oil for the Allies.
Well writing and documented.