The first sentence is incorrect, because "work experience" is uncountable. Replace "a" with "some", and it's acceptable.
The second sentence is acceptable American English and the third is acceptable British English.
"Vacation" and "internship" are used in America, although both are perfectly well understood in Britain. "Practical training" is more British English, but I imagine it must also be used in American English (and it must certainly be understood). "Holiday" has, in America, retained its original meaning of a religious festival and is often taken to mean Christmas and New Year. In this context, I think most Americans would understand what you mean, but it might sound a bit strange.