We have not rented strolers - always brought our own. Strollers can go on the monorails, and you can leave them open with the kids sitting inside.
If you have a double (side by side)stroller, you will need to find a car that can accomodate a wheelchair, or it won't fit through the doors.
Actually I don't their is a double limitation anymore the you have to have one that fits a wheelchair. The changed the Monorails so they don't have anything in the middle to block. At least that was my experience when I took the double.