You can take a SuperShuttle from LAX to the Disneyland area, as there are no hotels in OC that would run a shuttle there. I always see them while I am waiting for my downtown one to show up.

Try their web page http://www.supershuttle.com for information.

Even though SNA is closer, I don't think that any hotels run shuttles there either since it is still a 15-20 minute drive with minimal traffic.

If you do drive from LAX take the 105 east, to the 605 south, to the 91 east, to 5 south which currently is under a little bit of construction in the Disneyland Resort area.
Just avoid the 405 at all cost.