Im not Asian/Oriental (pick the term since they are in discussion), but I do have a number of "Asian" friends (used at random). I dont use either term, frankly, because if they are legal American citizens, then they are just Americans. No different than anyone else. Just like I dont recognize Mexican Americans or German Americans or African Americans. Are you an American or not? You may have come from someplace else, but that's irrelevant.
Regarding Asia or the Orient, if Im traveling there, I personally would say I am traveling to Asia (vs "the Orient") if I was going to more than one country, or else I'd say I am going to _______ as a specific country. A person who is a citizen of that country is _____ese, just like someone who is a resident of this country is American. Americans who hail from those countries are still Americans, they are just ancestrally from _______.