To be honest, your birthplace, ethnicity, and nationality are irrelevant, and it is not appropriate for people to ask questions of that sort in a professional context. You may not mind the question, but others may. By introducing the information as a preliminary, you are setting a precedent that will pressurise your colleagues who may prefer not to discuss the matter.
Personally, I do not generally tell people about my birthplace, ethnicity, and nationality in the course of teaching, unless it had some connection to the subject-matter at hand (e.g.: if I were citing my own experience/background to illustrate an argument I am presenting in the lecture -- I am in a humanities subject, so that does occur in some instances).
However, when I used to work in Scotland, I was open in declaring that I am not local (but without specifying much more), since my accent (British-English Received Pronunciation) makes it fairly obvious (although, as an ostensibly "neutral" accent, it does not tell you much more). When I mispronounced the Scottish name of one of the students, I apologised and added
"as you can tell, I am not Scottish -- in fact, I live south of the border"
(in the UK, it is quite common for academics to not live in the same city as their university).