Take the MTA to PATH to Newark Penn Station to Newark light rail. You can use your metro card for the PATH, I believe. I have never taken the path, so I'm not sure if it's speedy and efficient(I will assume so)
In the daytime, its generally safe to walk from the Broad. St station in Newark to NJIT. I did this for Rutgers: walk down Lackawanna Ave to the RU campus; NJIT is nearby. There is also the Washington St. Station that's near University Ave and a block from the corner of University Ave and Warren St.
I can't speak for at night, since I don't stick around Newark late enough to find out.
There are the
Rutgers Campus shuttles that make some stops a a couple of NJIT buildings. There is a shuttle to Newark Penn Station on the weekdays b/w 4pm and midnight to the NJIT and other college campuses. That may take care of the nightly walk to the Light Rail Stations.