Good question! Turkey was pretty weak during WW2 and couldn't have put up much of a fight if the Germans and Bulgarians had decided to invade. Had things gone better for the Axis, the Turks might have been coerced into joining the war on their side. They wouldn't have been very happy about it, though.
Turkish troops might have been somewhat useful in garrisoning occupied Soviet Central Asia, despite the certainty of very bad blood between their forces and those of the 15,000 man Armenian Legion.
Iran really wanted to remain neutral, and resented threats from the UK and the USSR. It would probably have happily accepted Axis help in resisting Anglo-Soviet occupation, which Reza Shah had hoped (in vain) that the US would somehow prevent, even writing to FDR and citing the Atlantic Charter. An Anglo-Soviet invasion of Iran, he said, was as much an unjustified act of aggression as the German-Soviet invasion of Poland. But the US cared nothing for Iranian neutrality. The routes needed to get Lend-Lease aid to the USSR, and the Iranian oilfields, which had to be kept out of German hands, justified the invasion.
Today, some scholars claim that pro-Axis feeling in Iran, shared by its Shah, frightened the Allies and prompted the invasion necessary, while others say that the pro-Axis sentiment was in fact caused by Allied threats to Iranian neutrality. In Iran, many people are still bitter about this invasion; Ahmedinejad has cited it as one reason for Iranian enmity towards the British.
We all know that the flight of the Shah to Iraq, to escape the forces invading his country, provoked the British takeover of Iraq, at least according to the British. Like Iran, the Iraqi armed forces resisted this attack furiously, although the end was never really in doubt.
Turkey, Iran and Iraq, while militarily weak, were valuable for their oilfields and strategic location, and would have made worthwhile assets, if the Germans could have taken and held on to them.