Yes, I've heard that people in Europe would often/sometimes use the term, "Oriental." With that knowledge, I personally would not mind that term at all if the people from there would use that term.
In Japanese, we actually have the equivalent terms, "Easterner" versus "Westerner," (the ones Wrlmy is referring to) which has often been used in socio-cultural discussions. I like these terms for the cultural connotations that encompass the history. It was an epoch making for Japan to have opened to the Western countries around the turn of the century. The cultural gaps between the West and the East have long been the foci of important socio-cultural discussions throughout the modernization of the country.
Although these terms are too broad and too insensitive to acknowledge the cultural differences between countries, I still find it a useful framework that captures some fundamental socio-cultural structures.
On the other hand, it might be possible that some negative connotations may be involved in the term, "Oriental," in the context of the US history. But I do not know the origin or historical context of the term at all.
At the everyday interaction level, however, "Easterner" and "Westerner" may sound a bit old-fashioned even in the Japanese cultural context. As I said, a lot of times, these categories are simply too broad to make any meaningful reference. People would be more likely to refer to each specific name of the country or narrower regional categories such as "West-Europe," "South-East Asia", "North America" etc.
In the context of the US, I have never heard the word "Oriental" be actually used to refer to groups of Asian Americans or Asians. AFAIK, the most "official" term (e.g., The Census, other surveys) would be "Asian" or "Asian American" in the US. They used to be often combined with "Pacific Islanders" and called "API" until several years ago. But they are now considered to be more separate categories. In addition to "Asians" or "Asian Americans," they'd also say "East Asians", "South Asians" etc when they want to be a bit more specific.
At an everyday interaction level, I have personally never been called "Asian". People tend to be a lot more specific. All those friendly people who talk to you on street or on bus would ask me if I was Japanese, Korean, or Chinese. But most likely, they'd somehow know that I must be Japanese.
I'd prefer when people are specific about my country of and ethnic origin at personal interactions. But this may depend on your personal backgrounds (e.g., level of acculturation, racially/ethnically mixed origins etc). Some people may prefer being called "Asian" or "Asian Amecian" than "Japanese" /"Japanese American" etc. I don't know.
Finally, my personal experience of being called "Oriental" was when an old White lady told me on street that I looked like an Oriental doll. Although I knew that she meant it to be a compliment, I felt a bit annoyed. Although I have never been annoyed by a "doll" or a "Japanese doll," her "Oriental doll" suggested some exoticism, even though I would not think that she was conscious about it. It sounded a bit old-fashioned as well. But then again, this may have been just a cultural expression to refer to East-Asian traditional porcelain dolls which might have been commonly used. In any case, this has been the only occasion that I heard "Oriental" so far.
But as I said, I would not be annoyed if the term is used in a neutral or a nicer way especially with the knowledge that it is used neutrally in the UK.