My nephew overstayed in the United States and received an order of removal four years ago. He never committed any crime and always maintained a good record throughout his entire stay in the US. He left the country himself (means that he was not escorted by the immigration officers or received a direct deportation). In fact, he didn't even know that he has a removal order. He's currently in Japan (his birth country) and is interested in completing his postgraduate degree in the UK. I believe that he would need to apply for a student visa in order to travel as an educator. My question is will he be eligible to apply for a student visa to UK with a record of a removal order in the US?
Your nephew is not automatically barred from applying for a student visa for the UK. However, the visa application will ask:
Have you ever been deported, removed or otherwise required to leave any country, including the UK?
It will be up to UK immigration authorities as to how, if at all, the US overstay will affect the visa decision.
He might answer that question with "don't know" and then add an explanation what actually happened. He was obviously not deported or removed. Whether he was "required to leave the country", when a removal order was issued but he left voluntarily before ever learning of that removal order is debatable - give UK immigration a chance to decide that maybe you were not "required to leave the country". In theory a removal order could be issued after you leave but before the issuer learns that you left.
(Obviously "required to leave the country" must have some specific meaning beyond the normal, because every single tourist entering the USA is "required to leave the country" within some time frame).