I think in the US, it really depends who you ask. University departments sometimes distinguish East Asia (China, Japan, Korea if they can afford people to actually study it ahem) from Southeast (usually covering at least Vietnam, Laos and Cambodia I believe - but sometimes more). Some outfits speak of Central Asia as being more the neighborhood of Kazakhstan. Or you can even hear "Southwest Asia" referring to possibly Iran or even maybe, Turkey. Quite a few people do have clearer ideas of these.
But in folk usage, when you say "Asia," it's amazing how people on the street still assume it must mean one very particular area. That gets silly enough to begin with if you worry about it though, as quite a few people are not all that clear on geography and they tend to simply neglect a country or two. Or confuse some. If you stop using precise terms over that sort of problem, then pretty soon you'll have to struggle with words like "Oklahoma" whenever one of the parties to the conversation grew up too far away and never became interested in geography.
I still see Oriental used quite a lot on hotel titles, advertising, and business letterhead. Particularly I think in more conservative countries such as China, Pakistan, Malaysia, etc. It's ironic because one faction of the same countries tends to be very busy (or even overactive) in shouting about foreign intervention or application of Western standards to local situations. I'm not sure how much of using the term is just for advertising exoticism, and how much is a celebration of claimed in-group history and "uniqueness." At some level, the conservative take and the entrepreneurial take go together rather well. It could also be partly because British English still has a great deal of influence in these areas -- that, and language education tends to lag behind the social trends that may have changed certain usages in the West more often?
Oriental often rings as rather antiquated by now in the US... People in academia tend to think immediately of Said's Orientalism and some will get nervous about anything that sounds vaguely similar, regardless of intention. Then again, I think in more pulp novels and even Western advertising, it's still fairly common as an exoticism and entertainment trope. Enough people may realize that some people really do mean to use it as a way of identifying with a particular setting. In my own book, it could even have some relationship to how Western academics still regularly write many Asian names with surname first (I mean while writing analyses otherwise largely in English), in the style of the languages they are translating -- that's still considered quite normal, though I find it pretty incongruous myself.
Anyway, speaking of individual persons or from a distance of customs, Asian generally comes off better than Oriental. At least, I would say that's true in the US in communities that are sensitive about race and colonialism. But there's some room for more exotic advertising, literary, or perhaps personal renditions of Oriental I think. It hasn't completely gone away and I wouldn't go quite so far as to insist it should. So it's sometimes a trick of the situation and relationship involved.
From one angle, it could be rather like knowing when it might be safe to use Black. Or let's say more, precisely what context and tone of saying Black -- the word itself is quite common, but getting it across well is perhaps not so simple. Or even the much more troublesome and by now, historically burdened word "nigger." Yes some people do use it, though it's usually accepted mainly among Blacks in their own dialects which is a very exclusive game. Unless I suppose, just maybe you are living in the ghetto yourself day to day or perhaps in deep with a clique of people who have adopted more sort of Eminem style. Something where you are feeling pretty darn sure you won't get your head bashed over it.
Even then I think I'd be a little worried about hitting the note just right... I tend to think the cocky people on such scores often enough run into someone not from the same background and make them think, "Wow aren't they racist [or sometimes, playing it up awfully hard for no good reason]" And we do get plenty of people -- who often enough appear to be somehow or other biased btw -- trying the "I've got some [insert minority] friends, so clearly I can use this otherwise volatile word and everyone should know I couldn't possibly have the wrong idea anywhere in my life no way no how." Which can quickly get ridiculous the more it's played, if it isn't actually a cheap excuse to begin with. So... Oriental, I would say, is not at quite that level of controversy. We don't so vehemently say, generally "Just don't play around with it" with quite that same sense of terror. It's not subjected to quite the same level of scrutiny or the same general presumption of ignorance or hate. But there are situations where it could really go amiss for similar reasons.
Again, it doesn't quite infuriate me to see Oriental in a hotel title, although I may smirk and roll my eyes slightly. Especially if I feel they are overplaying it or taking themselves too seriously about supposedly knowing esoteric things I have reason to suspect they are clueless about. It's more when it gets applied to individual people, I might sooner perk up and ask why now.