Some people are overly sensitive about everything. I'm Hapa-Haole, half Japanese, half white (you know, pretty good at math, but can't grow a beard), in some circles the term Hapa-Haole is very derogatory, but the Hawaiians I grew up with used it as an endearing term, since nearly everyone we grew up with was the same.
My mother used the term Oriental, she was 100% Japanese. I don't know anyone that seems offended by it, but I do know a guy that gets extremely offended if you say Jap (which my brother and I use freely referring to each other), but that is only one guy. The rest of our Hapa-Haole friends don't really seem to give a shit about any labels that people put on them.
One thing though. Don't ever refer to a Japanese person as Chinese, that is an extreme insult. All the old Japanese people I used to know (they're all dead now), didn't like being called Asians, they felt it lumped them in with Chinese, Korean, Vietnamese, etc. They were almost like Nazis, the Superior Race. Nice Nazis, but still pretty racist. 100% serious. One of my friends father or uncle once said, "Do you know the difference between a Japanese perskn and a Chinese person?" "A Chinese person is a Japanese person with half his brains beat out."