Skip Soda Lake Rd. and ride Elkhorn Rd./Elkhorn Grade Rd instead. It's on the East side of the Plain Soda is on the west and down in the "valley". Elkhorn is much more picturesque and you won't get bored passing all the minivans stuffed full of tourists.
I've ridden both and prefer Elkhorn...incase you couldn't tell.
You can gas up 6miles off 166 along Hwy33 at the Santa Barbara Pistachio co. and get some bomb ass Pistachios too. They only have regular gas. If you need premium, you'll need to head to Taft a few miles past 166/33 junction Pick up Eklhorn Grade a mile or so West of Taft. Elkhorn Grade connects to Elkhorn Rd at this intersection:
Take the right fork. The left will lead you over to Soda Lake Rd eventually which is just over the hills you can see on the left in the pic. It's 45 miles of gravelly/sandy/rocky fun. The sand isn't bad. Big bike loaded with gear is no problemo. As you near the North end of the plain, check out you GPS and have a look around you...why is that street sign in the middle of nowhere?