I'm a greencard holder and I want to visit Middle East. What should I do?

Yes , you must use your Iraqi pport to travel internationally. You will use your green card to get back into the U.S. Both must be current. You cannot stay out of the U.S. more than one year without needing a re-entry permit. See 1st site below and read paragraph on International Travel. You may need visas for the countries you plan to visit. How long they permit you to stay is up to the country you want to visit. You can use the 2nd site to see if you need a visa to each of the countries you plan to visit. It wil also tell you how long you may stay in that country. Just enter your nationality, enter that you are an alien resident in the U.S.A., enter your destination and click for the info. I tried to check for you just now, but their system is down right now...so try later. Ah...found the info on the Lebanese emby site...see 3rd site below. it specifically says you may get a visa on arrival...read all info there.