Yes, renting a car is by far the cheapest means if driving is an option.

Otherwise, try the "business class" service offered by Express by ExecuCar. You should be able to get from LAX to central Irvine for about $95 (exclusive of tip). It's a minivan, but it's a private ride.

My most recent research for transport between OC and LAX found them to be the cheapest alternative by far (other than the FlyAway bus, which never works for me, as I usually need it before or after operating hours). I checked towncar/limo services, taxis and shuttles (yuck). I've used them twice in the past two months and was satisfied with the quality of the service for the price.

ExecuCar is owned by Super Shuttle. They only honor a few promo codes on the business class service, but when you find one, it's generally worth about 5% off. You can earn UA miles, too.

FWIW, I took a taxi from LAX to the South OC about a year ago, and it ran wellover $150 before the tip... I'm pretty sure central Irvine would run you closer to $125 than $95 these days, and that's assuming you hit zero traffic delays. YMMV.