Xibei San Ma
This is the only scenario in vanilla when you have any chance of success as Iraq. For you are not a puppet of the United Kingdom. As Iraq you have the terrible shadow of the soviet union above you, and depending on your aggressiveness level, will be happy to put you down. Firstly, you must build a small militia army and move sliders to a more authoritarian stance. This will cause less dissent when you declare war on your first enemy - Iran. Without full IC take over this is harder than it seems. Iran (also known as Persia in vanilla) has a small army but has VPs all over the place. It's best to rush and cut off Tehran and watch the rest of its armies fall. Then annex.
There are now 2 possible routes. One is the very risky route. Declare war on Afghanistan and defeat them (easier said than done, the terrain is just awful). Then head through Sinkiang and try to get as far into China with your now brothers, the Japanese. Getting a large portion of China is nice to see on the map. The second route, can also be done if you finished the first route fast enough. When Vichy is created, Syria and Lebanon form. These are weak states, easily gobbled up the quicker you are able to. Take them of course. Now it's leading into 1941, your army should be nicely experienced and sized and you're ready to strike through Turkey and into the Balkans. Join the Allies if you like, but you may run the risk of the Soviets then declaring war on you, along with the Allies... leading to a very tricky position indeed.