I don't know what Iran was like during the war, but I assume it was not the same kind of power they have today. Iran today is a regional power, while I don't think Iran during WWII had the power to influence much of anything even if all their neighbors were independent, which means alliances will be all the more imporant.
I could see you allying the Turks or Chinese if you have the chance. Then aim for either the Caucasus or Iraq/Persian gulf Arabia (which requires war against either the USSR or Allies). Unlike Victoria II, since strategy and tactics are very much important in Hearts of Iron IV (obviously), I believe it might be easier to tackle great power if they are distracted and you use good tactics and judgement (after all, the Middle East include high attrition zones, and the geography of the Persian Gulf can allow you to quickly grab any nearby ports).
After you get the oil rich provinces, LIBERATE any further nations you get (or maybe puppet, that would be better). Iran is not in a position to administer such huge tracks of land, and should have 100% of its military fighting actual enemies instead of unrest. Not to mention the autonomy of a liberated or puppet nation in your faction would be a burden off your shoulders. Liberate Syria, Egypt, Jordan, Lebanon, Georgia, Pakistan, Turkestan, etc. and whoever else is convenient.
Getting China on your side might be a godsend as long as you actually help China against the Japanese (China could use Iranian troops, and your support might be able to turn the war in favour of China). If you manage to ally China, finish off Japan first so that China can put 100% of its attention in helping you. Another good thing about fighting Japan is that you don't need too much in terms of vehicles, since Japan is only partially motorized, not fully mechanized. Holding off Japan at or near Beijing also gives China extra time and resources to quickly industrialize just a little bit extra to become stronger.
