Oh, my goodness, this is a minefield! It depends on so many things. The interpretation depends on where you are geographically and culturally, what period of history you are talking about, who you are talking to, and (potentially) how politically correct/polite you want to be.
In the UK, 'Asians' generally refers to people from Pakistan, Bangladesh and India, as these are main ethnic minorities we have in this country. In the USA, 'Asians' tends to be used for people from China, Japan, Korea and neighbouring countries.
'Orientals' makes it clear that we mean people from what has traditionally been called the Far East, namely, China, Japan, Korea and neighbouring countries. However, this is an outdated term and it is can be seen as mildly offensive these days.
The word 'Easterners' doesn't mean anything much - it seems too vague. Although it would seem to be the opposite of 'Westerners', I have never heard it used.
Here's some advice - avoid using nouns like this as much as you can. It's more precise, and more professional and respectful to say 'People from...' and then specify the particular country or region.