Whoops! I missed the "incomplete" portion of your message. That is truly bizarre. Do you have any idea which components of you application are incomplete? I'm not familiar with MIT's system, but most of the schools I've applied to will list the pieces of the application that have (or haven't) been received.
It is a little frustrating that there isn't anyone you can contact at MIT to get additional info about the problem.
An on-campus interview is just that: an interview with a particular program conducted on campus. I don't know if it is common or not (perhaps someone else on the forum can speak to that issue). It is my understanding that some schools conduct them and some don't. I would imagine the process is a little different for domestic vs. international students.
I'll provide more details about the specifics of the event when I get back.
If you haven’t done so, I would recommend taking a look at the PhD Strategy thread on the Business Week website. There is a wealth of info related to the application process amassed there. It might take you a couple of weeks to get through.