Is there a fast/cheap/comfortable way to get from LAX (Los Angeles International Airport) to Irvine or South Orange County?
For a while this service was provided by the FlyAway bus but the LAX-Irvine service seems to have ceased operation.
It depends on how you weight fast/cheap/comfortable and how far south you'd like to go.
My suggestion would be to take the FlyAway bus to Union Station ($7, ~45 min), then take Amtrak's Pacific Surfliner, which starts at $17 to Irvine (59 min) and $22 to San Clemente (88 min). The Pacific Surfliner is reliable and clean, and bypasses the 405 freeway's notorious traffic. There is WiFi provided, although reviews of it are mixed. A cheaper alternative is the Metrolink Orange County Line, though there is no WiFi, and the trip is slightly longer as it is a commuter train and will make additional stops.
You could also take an airport shuttle and save a little bit of time for about twice as much money. The main advantage is that you're on the same vehicle door to door, so no waiting or luggage fumbling during transfers. South O.C. is a long way from LAX, however, and you may be forced to wait while they fill the van and while they drop off everyone else. Best case scenario with no traffic, you arrive in Irvine in an hour, but it can easily be triple that. The two shared ride van concessions are currently SuperShuttle and PrimeTime, and there is also Mickey's Airport Bus if you reserve in advance.
It is a pretty straight shot down the 405, but getting a one-way car rental from LAX to SNA can vary considerably in price. I just tried it now and was quoted $96, and after adding fuel and insurance it would be more convenient simply to take a taxi, which Taxi Fare Finder estimates at $150.
There are other combinations of buses and trains that are possible, but these will take considerably longer and require multiple transfers. My favorite way to get from LAX-SNA was by Embraer 120; sadly, Skywest (dba United Express) discontinued those flights years ago.
Super Shuttle and Prime Time Shuttle offer shared-ride vans between LAX and many cities around Los Angeles, including Irvine. The ride will probably take about an hour or so more than direct ride because of dropping people off in different parts of the city, though they usually do a good job of grouping people by location. I did a quick estimate for Super Shuttle going to Irvine, and the cost seems to be around $50. You can make online reservations, although you can also just show up and follow the signs. I suggest making reservations during peak travel times.
Parking is free at the Anaheim Amtrak station if you purchase an Amtrak ticket. You do have to notify security with your information for parking. Then it is an easy transfer to the FlyAway Bus at Union Station. Recently cost me $44.50 (AAA discount for roundtrip Amtrak ticket and $8 each way for FlyAway) for all tickets and a week worth of parking at the train station.