The federal courts still have the death penalty. But the gallows is out I'm sure. Firing Squad or Lethal Injection.
As for whether he'd be tried in a US Federal Court, or Military Court (I can't see that), or Iraqi court remains to be seen.
His crimes were against the US and it's allies, however, they took place on Iraqi soil - and since Iraq is (supposedly) self governing now - or at least has a government a court system - they might wish to retain authority to try him. Either way, he will be dealt justice.
I'm not sure there is a "Status of Forces Agreement" in place as there is similarly between the US and Germany. I recall being told when I was living there to ensure I had my "SOFA" card when I ventured into the countryside. Should something untoward occur, I was to present it to the German Authorities and it obligated them to notify the US military of my situation. They would then decide who had jurisdiction. Most often the offender was turned over to the military for minor offenses. Major crimes were left to the hands of the German people.
Personally, I think since the crimes occured on Iraqi soil, the Iraqi Courts have the first "right of refusal" on the issue.
FOR THOSE THAT FOUGHT FOR IT, FREEDOM HAS A FLAVOR THE PROTECTED WILL NEVER KNOW OR UNDERSTAND