I ran most of route 66 on my run across America in 2010 www.runforliberty.com
Route 66 was amazing and I have TONS of great pictures. Running and riding is NOT permitted on the interstate in CA. At least that was my experience. It IS permitted in the rest of the states that 66 goes through, which is good since many sections of the mother road are not intact. I love to talk about it if anyone has any questions. I feel like I became very intimate with it only cover about 25 miles a day on my feet.
I am now planning an epic bike tour of some sort. Cycling sure gives you more freedom to see more things, but to be honest, it moves a little too fast sometimes for my liking 
Nice running trip!
Actually, cycling is permitted on the shoulder of about 1000 of the 4000 interstate miles in California. It just so happens that very few of these allowed sections coincide with Route 66. But all of these 1000 miles allowed by bike may be off limits to those on foot. On my Route 66 tour, I had a climb on I-40 westbound out of Needles for about 20 miles, before existing at US95 and returning to the old Route 66.
On another note, I may be going to Gallup, NM sometime on business and might have the opportunity to ride Route 66 from there to either Flagstaff, AZ or Albuquerque, NM. Thoughts?