I am a PhD student at a research institut in Switzerland, and registrated as PhD student at EPFL. As my contract with the institut will finish at the end of April, but the PhD thesis Jury defense will happen in early May and public defense in June.

The institut said that after April 30th, you have no relation with the institut. My professor at EPFL just said that she would issue a letter which states the evolution of your thesis and the deadlines which lie in front of you.

I am holding China passport, how should I deal with such situation about staying in Switzerland for thesis defense. Is it possible that I can apply for Permit B prolongation with that letter from EPFL? if not feasible, how should I apply for a VISA to Switzerland?

Check with your canton migration office. This problem seems to come up fairly regularly and they're the best people to advise you.