If he believes that it is an "illegal and immoral war", then any order requiring him to fight in it would surely be an illegal order, and he'd be morally and legally obliged not to obey it.
However, while the initial invasion of Iraq may well have been illegal and immoral, it's extremely arguable as to whether ongoing operations in Iraq (peace enforcement, aid to the civil power, etc.) are in any sense illegal. Badly-led, ineptly executed, counter-productive to the USA's national interests, dangerous and unpleasant, perhaps, but illegal?
Aren't US forces now there at the express wish of the Iraqi Government, such as it is?
And if it is illegal, then could he not be sent somewhere else, equally dangerous, and equally unpleasant (Afghanistan, perhaps?).