I found this article on the subject. Unfortunately, it doesn't look promising.
ZNet |Japan | Open the Door -- Japan's Policy of Exclusion of Refugees
I don't know your feelings towards the United States but you may want to consider applying for refugee status there. I can understand if you have objections. I know that if the tables were turned, I wouldn't appreciate anyone occupying my country no matter what the reason.
However the US still has one of the most open refugee policies in the world. Canada is the only other country that I can think of that is more open. You should also check there.
I am only making these statements under the assumption that you simply want to get out of Iraq and are simply looking at your options.
No matter what you decide, I wish you the best and hope for safety of yourself and your family.