I think you might have a problems to grow anything under the walnut due to juglone issue, but oaks are friendly and Cl. hydrangea (Hydrangea petiolaris or Schizophragma hydrangeoides) will feel very comfortable with your lighting conditions.

Here is a link that might be useful: Walnut and Juglone

Dutchman's pipe (Aristolochea sp.) might get by with dappled sun. It is said to be tolerant of part shade.

clytostoma callistegiodes (sp?) or Violet Trumpet vine is evergreen and shade tolerant. It's native to south America, so it should not become invasive in CA.

If you are going to plant azaleas, rhodies & camellias you may want to have your soil tested first...they need acidic soil. Though all of the oaks may very well make the soil under the trees acidic before investing in all of those shrubs I'd make sure.

You may need to be careful if they are CA oaks. Those will die from summer watering, and even drought-resistant plants must be watered in the first couple of summers.

Google for a list of plants that are considered 'oak friendly'. You really want to save them, they are fabulous trees.

I have not had any problems planting a variety of plants near walnut trees -- black walnut trees release more juglone than English walnut trees. My biggest problem planting near them is that they absolutely suck up all the water under the canopy, and plants and shrubs have a hard time competing with the tree roots. I have callas, erysimums, limonium, star jasmine, nasturtium, alyssum, cannas, phormiums, and agapanthus around our walnut tree.