Here is an AP article on the status of US forces in Iraq. AP reports:
Washington has an agreement with Baghdad on privileges and immunities for the growing number of troops based in Iraq who are helping in the fight against the Islamic State group, the new U.S. ambassador said Thursday. In an exclusive interview with The Associated Press, Stuart Jones said Prime Minister Haider al-Abadi has given assurances that U.S. troops will receive immunity from prosecution. Under Iraq’s former Prime Minister Nouri al-Maliki, that issue was a major sticking point, ultimately leading to the decision to withdraw all remaining U.S. troops in late 2011.
No word on that status of contractors supporting those forces or if “US forces” includes civilians supporting uniformed forces, who are fully subject to Iraq law after the expiration of the US-Iraq SOFA.