In this alternative history, the Japanese commander has all the troops, equipment, ammunition, naval support, and supplies as the IRL Japanese commander had.
In this alternative history YOU are the commander of the Allied forces invading Iwo Jima. You have at your disposal all the troops, equipment, ammunition, naval support, and supplies the IRL allied commander had. PLUS you have 3 dinosaurs that’ll only attack Japanese troops.
So, what dinosaurs would you want?
I’m thinking something like an ankylosaurus might be useful in burrowing into the tunnels the Japanese were fighting from.
I want the raptors from Jurassic Park. Unless the Japanese have motorcycles they’d all be screwed.
Just 3 dinos? Aside from maybe a handful of extra kills out of 10s of thousands, I don’t see how any of them would matter. I doubt even the biggest would survive more than a few mortar rounds. Thier corpses might have made good cover on the beach though.
I love ankylosaurs, but I doubt an animal who walks forward but fights backward is ideal for fighting in confined spaces.
Mindful of the fact that Japanese weaponry would quickly kill any real-world dinosaurs, I’m bringing Tyrannosaurus Rexes trained to smell explosives. With their enormous nasal passages and large olfactory bulbs in the brain, they are believed to have had a phenomenal sense of smell. I will hold mine back from front-line combat and use them to suss out boobytraps and hidden “stay behind” troops in spiderholes.
Plus, if one of them can reach the flagpole with his tiny little arms, think of the propaganda and recruiting value of having a Tyrannosaur in the iconic flag-raising photo!
I’d choose a spinosaur (preferrably* Spinosaurus Aegyptiacus*) any day. While largely aquatic (and thus being able to swim ashore, needless of supporting amphibic vehicles) it is large enough to stand its ground on the beach even in fire from small arms and is capable of killing a lot of enemies (and frightening the shit out of a lot of more)!
Unless it’s Godzilla, never mind. Zero strategic effect.
Now that’s just stupid. Godzilla didn’t mutate until after nuclear tests in the 50’s. Stick to the realistic OP! 
Would you believe Leviathan?
Do any dinos fart poison gas? If not, forget it. That’s the tactical choice I would make at Iwo - gas the whole island for a week or three. It’s not like there is any civilian population to worry about.
Does Titanoboa count? I would use a couple of those to attack the Japanese fortifications and caves. Otherwise I would take something small and vicious like a Velociraptor that can rush into caves or through a firing port and attack the enemy in their hidey holes.
Otherwise, it is kind of pointless. As others have pointed out, any large theropod would just get shot. And while the fighting on Iwo Jima was terrible and vicious, the Japanese were doomed from the start. It would make no difference at a strategic level, and it would take far more than three of any species to make a difference at the tactical level.