How do I alleviate the effects of salinity in irrigation water?

You need to flush the salt out of the soil and then with salty irrigation water you will need to continue to flush it out over the coming years. Tile drainage and plenty of water to flush the salt down to the drains is the answer. If you continue to have problems with sodium clinging to the cation exchange you may need to apply gypsum and then again plenty of water to flush the sodium out to the drains. The gypsum floods the soil with calcium that can kick the sodium out so it can be flushed. I don’t know where you are in CA, I would guess you are in one of the drier areas. In my area of Northern Utah our soils were salty when they started irrigating. With the addition of irrigation water it brought the salt to the surface all the more because the water had no where to go but evap from the surface. So they started putting in tile drains and while they waited for the salt to work its way out they grew salt tolerant crops like barley and sugar beets. Now we can grow almost anything.