How common is it to get an academic position in a different country after getting a PhD in the US? For someone who is doing his PhD in a US institute (STEM filed), how likely is it to be employed (as a post-doc for example) in another country (which is not my home country, in general) ?

For example, for a PhD student, it should be much more easier get a job in an environment that you know; for example, the school that your are doing own PhD, or some other instituted that you are familiar (possibly in US also), but, in general, is it common for such a student to get employed by an institute in Europe or elsewhere?
I wouldn't think there would be discrimination either in favor of or against a PhD from any particular place. That isn't how people make decisions about who to hire. Instead, they will look at what you have done and whether they find it "interesting" and "deep". You can produce such work anywhere and it will be valued everywhere. 

In any application, whether for a degree or for employment (a) there will likely be a lot of competition and (b) you need to make your case. These things aren't decided by plugging things into spreadsheets, but by  people looking at your output and your perceived potential to contribute. 

That said, you may need to make sure that you speak the local language and are comfortable in the local culture. If a job involves teaching, for example, not speaking the lingo may be disqualifying - at least in some minds. But even in a non-teaching position, you will be expected to interact with others in the institution. Don't take a math postdoc in, say, Italy just because you want to begin to learn Italian. 

I recognize that I answered a slightly different question: How difficult is it... I hope that serves your needs.