i did Los Feliz to Santa Monica for a good amount of time. Most of the ride was on Olympic. it was a little sketchy at times, but you just have to take control of your lane. when the traffic is heavy - aka, at a standstill - i would usually cruise between the middle and right most lanes. there's always a nice gap between the cars!
now i take sunset to downtown, and there is a bike path most of the route, which makes things somewhat easier. definitely less worry about finding room to ride in.
just stay off the sidewalks - that is the general rule. a friend of mine was hit pretty bad becuase of riding on the sidewalk. stick to the street, and let the cars know you're there.