What is academic degree after PhD? Does your country have any academic degrees after the PhD? If yes, what is it called and how graduating this degree? 

Additionally, what is a Post-Doc? Is it a degree or something else? I have seen some people refer to a post-doc in their CV as they would a degree. Is this acceptable?
In general, a PhD is the highest degree you can get. A postdoc is simply a research position that is not permanent, i.e. no fixed contract or tenure. There are some exceptions, for example in the German system where you can get your Habilitation, which is a degree after you get your PhD. But in most systems there is nothing beyond a PhD in terms of degrees.