Your nationality may make it easier to gain admittance, such as if the university is actively trying to recruit international students. However, you should know that your tuition fees will be that of an international student, which is often 3 to 5 times the price of an in-state student. However there are also scholarships and bursaries that exist for international students, maybe ones dedicated to Romanian students, etc.
When it comes to the big universities you’ve listed, it really comes down to your own skills, and to some extent, your grades. Basically, if you’re a diamond in the rough, you’ll have no problem getting in. If you’re an average Joe, well it doesn’t hurt to try, but don’t expect them to get excited about you. If you’re a bad or weak student, don’t even bother, competition is just too high.