This type of question is one of the main reasons that the US Government came up with the 'ESTA' program.
When you apply for an ESTA, it will prompt you for details of things like where you were born, your current and past citizenship status, as well as whether you've ever held a travel document for another country.
Once you enter all of the details, one of three things will happen :
- Your ESTA will be approved (almost) immediately.
- Your ESTA will be approved, but will take a few days for this to occur (which is generally a sign that it is being manually reviewed), or
- Your ESTA will be rejected.
If your ESTA is approved, you are good to travel to the US. Technically having an ESTA does not provide a guarantee of entry, but presuming you answer all questions truthfully when applying for the ESTA, then the odds of being denied entry under the Visa Waiver Program is so close to zero to basically be ignored.
If your ESTA is rejected, then you will need to apply for a visa. The fact your ESTA was rejected will NOT count in any way against your visa application, so there is no reason not to try the ESTA route first - it is faster, cheaper, and significantly less effort than applying for a visa.
I can't help you determine if you are or ever were an Iraqi citizen. In practice, you best option there is likely to contact the local Iraqi consulate and ask them, as they will be the best source of truth for that question. There's just too many variables that could be in play to base it on the information you've provided.