I never heard about TOEIC, interesting.
In my experience I know that if you are taking The TOEFL iBT test you need to have 100 or 110 out of 120 to get into an American university. I don't know if they accept the IELTS exam, because every Uni has its own requirements.
I know that the Cambridge English Examinations (CAE) it's a really good test either, but again, you have to be sure what exams they accept and then you can choose which one is suitable for you. You have at least 4 choices.
Normally the universities have a link that it's called "Aplication requirements" and there they summarize everything that you have to present when you aplly.
As an example you can watch this girl videos (she took the TOEFL and she applied to an American Uni) check on Youtube this channel "linguamarina".
I hope it was usefull. Good luck.