No clearance is required to enter Class C in the US, only two way communication. If they tell you to remain clear, remain clear, or else you put your licence in jeopardy.
As mentioned, SOCAL provides ATC services for Southern California within the LA basin and down to the border with Mexico. They fill the gap between LA Centre and the tower controllers. They have a huge amount of traffic to manage but will fit the little VFR traffic in with pleasure. The frequencies are on the terminal charts, but if you get it wrong they will advise you of the correct frequency when they find out where you are.
As Englishal says, they will suggest stuff if you are starting to get in the way, they cannot make you do things in class E. If they call you with a "N12345 descend at pilots discretion" it means if you remain at your altitude they are probably going to have to shift IFR heavy iron around you. Be polite and descend, letting them know where you will level off.
They would rather you talk to them than stay silent squawking 1200. Give them a call, they are nice people and very accomodating to the little guys.
Yes, they sure do it different.