I currently hold a one year student visa and a permesso di soggoirno which will all expire in October 2017. The student visa was issued to me last academic year but the DOV of my diploma was delayed and for that reason I couldn't enroll last academic year, now I have the DOV and a new admission letter. Enrollment for this academic year will start in September 2017 and my student visa expires in October 2017, can i use the same student visa to enroll? If not, I would appreciate if anyone can help me out, because I don't want to go back to my country and start the whole process again.
Academic institutions, like employers, have a duty to perform due diligence on applicants and their eligibility to study or work with them.
As such, if your student visa expires during the time you'll be studying (and it sounds like it will), you'll need to work with the university and your government to see if there's a way to extend it. Otherwise, you will need to get a new one.