Whitney hiking permits are still valid. Individual sites at Whitney Portal are still open if you can reserve a spot, it appears that just the Group sites that are not going to be available this year.

I know people do sleep in their cars. Here is a thread:http://www.whitneyzone.com/wz/ubbthreads.php/topics/38789/all

Other options include Individual sites at Whitney Portal or free camping anywhere in the Alabama Hills off Whitney Portal Road.