Oriental is still not uncommon in the UK, but if you were to say it in the US then it's almost a racial slur, which is largely due to the history of the word. 'Oriental' on its own was never intended to have a negative meaning, but because people used to use the term when talking about how different or strange Asian people were it gained a racist connotation.
Consider the term 'Jap'. It seems innocent enough because it's just a shortened form of 'Japanese', but during World War II Americans referred to Japanese people as 'Japs'. Because Japan was the enemy of the US, 'Jap' therefore became a word of hate throughout the country, and these days it is considered very offensive to call someone a Jap.
These days, it's acceptable to use 'oriental' as an adjective when talking about objects, like a rug or some food, but never a person. To be on the safe side, I'd just not use it at all.