I assume when you say work visa, you are talking H-1B. I’m not that familiar with all the details of J-1 Exchange Visitor and H-1B Temporary Professional Worker visas.
Generally, if she is here on a valid non-immigrant visa and marries a U.S. citizen, she normally would be eligible to adjust status to Permanent Resident. There may be some consequences though, such as losing her J-1 or H-1B status while the AOS is being processed. I know that some H-1B’s can be sponsored as immigrants by their employers also.
If you do get to the point where you want to marry while she is in the U.S., I would sit down with an immigration attorney for a consult to discuss the various options available because some of this stuff gets very complicated. I think Gary Bala will do a 30-minute phone consult for only $50 (bargain!)
As far as her parents visiting, they would have to apply for visitor visas. Parents are not considered dependents for the purpose of derivative visas (e.g. H-4).
Your situation is pretty unique and sounds like an interesting adventure. Keep us posted on what happens.
Ray