In my 00 Civic Si I just put blankets, towels or a drop cloth in the back and put my tires back there, but in most cases I drove to the event on them (Street tire class).

This is how I packed my car for NE Divisionals:
-tool box behind the passenger seat
-Harbor Freight lightweight jack behind my seat
-tires/wheels stacked vertically (all 4 fit fine)
-helmet, shoes, gloves in the passenger's side foot well
-2 Rubbermaid tubs with my emergency stuff (rain coat, extra socks, extra shoes, air pump, air gauge, numbers, larger sockets (didn't fit in my tool box), and other misc stuff) in the trunk
-air tank in the trunk
-had a Yakima bike rack which I took my mountain bike with me on

I also tried carrying my tires/wheels on my Yakima rack (next to my bike) using their Cargo Clips and two 2x2 pressure treated wood. I placed the wheels/tires facing forward on the pressure treated wood and rachet strapped them down to the Yakima rack. It was ONE big sail, but that was for another divisional event where I actually stayed two nights so I had luggage.