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.
Indeed, as mentioned in Pieter's answer, the university will have an office that is supposed to help you with this (often called International Scholars Office or something of the sort).
It does happen that administrative offices are not always as helpful or responsive as they ought to be. As a postdoc you presumably have a mentor or PI at the university whom you will be working with, and they have a vested interest in making sure you can start work on time. So I would reach out to your mentor and let them know you are having trouble getting what you need from the international office. If there are specific deadlines that have to be met, include that information, to give a sense of the urgency. They are likely to be able to prod the people in that office and help move the process along.
Keep in mind that this is usually the same office that handles visas and other matters for international students, and the school year is just about to start at most US universities, so the office may well be flooded with issues related to incoming students. As such, they may be able to be more responsive after the first couple weeks of the school year, once the flood eases. But it's not clear if you can afford to wait that long.