It doesn't sound like a good situation. With all the noise you hear, it sounds like you're living in an UNSOUND building. I don't live in CA but I'd suspect that if this was NEW construction after the '95 earthquake, there'd be at least be some 'block' between the walls.
In any event, if you're hearing simple sounds, then trying to dampen or even eliminate heavy sounds would be a project (IMO). MY $.02 says to move to a house/condo/apartment that has block or brick between walls and sound baffels between floors. (Or some sort of real soundproofing.) If you lived in MA, I could refer you to one such place. It was awesome because you heard nothing! BUT, I'm sure that when, and if, you move again, you'll know what questions to ask. Be sure you can verify any 'claims'. Taking someone's word could be disasterous. Where I use to live in MA, I could see the brick (I didn't have drywall), and I 'tapped' the concrete baffels on the ceiling and could hear the echo. (The baffels carry the sound to the 'ends' and they are absorbed.
Don't know what else to say. If you're renting, the owners may not allow you to do anything. My best to ya and wish I could help more.