How to file for educational expenses when the foreign university does not have a Federal ID # and have not issued 1098-T for the educational expenses?

If the university is not a qualified education institution you can’t receive education credit. The school should be able to tell you if it qualifies. Or you can check here. 

https://ope.ed.gov/dapip/

Thanks for your response. The school Massey University in New Zealand is qualified for getting financial aid through FAFSA. But they told that they don't have a U.S. federal ID.

So, my question is if there is a way to enter educational expenses and get deduction or credit based on the money transfer documation that I have with me.

I checked the irs database and your school is an eligible education institution. 

When you get to the 1098-T entry, you can say that you don't have a 1098-T and there is an exception. The program will then let you enter the expenses without the form. And, you will not need an EIN.