I have no problem being associated with Indians and Pakistanis or Filipinos (though most North Americans do not think of Indians or Pakistanis as being Asian), but the usage of "Oriental" in North America in my view, is the equivalent of "Negro" when referring to other people, it's not necessarily an offensive term but it's a dated one.
American resident here, under no circumstances is the word "negro" considered appropriate unless you're literally a teacher (and you better be reading something like Mark Twain).
Oriental is also very frowned upon, especially in any larger city, even more-so the coast. It's largely viewed as lumping together several different cultures together that are only very broadly related by geography.
So yes, both words are considered offensive. Only the elderly can get away with saying them now without being called on it, and they'll get some eye rolls.
EDIT: And before someone says "Ah but Americans are so sensitive, yada yada," it's true, I live in Seattle, a very PC place. But you know who else is in Seattle? Wizards of the Coast. The word Oriental isn't going to be in a product's title period, it's not even worth debating.