Do universities in the USA help postdoc researchers with the visa process?
Yes, they should help you with the visa process, at least to some extent. In fact, they will likely have to sponsor your application. You will probably require a J1 (non-immigrant) visa for a postdoc in the US. More information on how to apply for such a visa is provided here.

In short, you will need a designated sponsor. Your university likely has this status. They have certain obligations to support and monitor your progress during the stay. If the university has an international office, they can likely provide you with more detail.

In any case, for you to apply for a J1 visa, you will need to have a copy of Form DS-2019 provided by the university. This is issued by the designated sponsor, confirming your eligibility for the J1 visa program, and contains some details about their exchange program (under which postdocs from abroad will typically fall, if my understanding is correct), start and end dates, and how your stay is funded. Without this DS-2019 form you cannot apply for the visa at the embassy. You will also need to bring it to the interview at the embassy, where the consular officer will evaluate your application.

One important thing to note is that if you will bring dependents with you (spouse or child), they will need their own DS-2019 forms to apply for a J2 visa.