I am currently in Italy and I have a student's visa that is valid until the beginning of October and I received my permesso di soggiorno that is valid until the end of the year. Can I stay here after my visa expires or I have to return to my country before?
This resource states that a person can stay in Italy until the expiration date of their permesso di soggiorno. This is one of the best documents I found in English but can't verify the credibility
Does permesso di soggiorno override the visa?
Yes it does, meaning your permission to stay expires when the permesso does.
While the visa is valid, you can use either that or the permesso to enter Italy, but after the visa expired, you must use the permesso.
If you want to stay for longer, you Need to apply for an Extension of the permesso