My Oriental wife tells me that the term is outdated, akin to Negro describing someone of African American origin. There are negative stereotypes and connotations associated with the term.
My wife is personally not offended by the term Oriental, but did point out that census forms and other questionaires asking for racial background do use Asian American as the classification for that ethnicity.
I am not an cultural anthropologist (IANACA), but I think the "European" analogy is somewhat of a stretch since European countries are today somewhat homogenized, at least politically and religiously while there are no similar bonds between coutries that would comprise the "Orient". Also, I am not a geneticist (IANAG), but there may be more genetic variation between the different Asian contries population than between countries in Europe.