I want to wish you luck in your flight. You did not indicate if you had to change planes or if it were a direct flight.
Most of your difficulty will be in the terminal, not the plane. If your children are prone to sleep when you travel by car, they will most likely do the same once the plane leaves the ground. Most flight attendants will not mind keeping an eye on your children while you take one to the restroom.
A word of caution.....everything you carry on with you, you have to carry off. You only have two hands. Fortunately, all of your chldren can walk on their own with the exception of the one year old. You could prepare each of them an entertainment backpack. Expect to wait to deplane last as people will be impatient and you will want to have each child put the back pack on before leaving the plane so you don't have to carry it. I would recommend getting the clear ones from Wal Mart so when they go through the scanner you won't haev to empty them. Check with the air lines to see what is permissible. I took some embroidery on a plane with me once and they made me throw away the small scissors I had with me!! Kinda defeated the purpose of taking the embroidery as I couldn't cut the thread when I finished a design! You might want to get a fannypack or even a backpack for yourself. I recommend the fannypack as your personnals will be at the ready and in a location where you can easily keep an eye on them (pickpockets and all at airports). You will no doubt have a diaper bag so you could put your personal items in the bottom of the diaper bag so you are only carrying one bag, they now make a fannypack diaper bag called a "bandlier" I think. It is large enough to carry all your essentials for a short period of time and might work perfect for this trip--freeing up both hands for children. :-)
I caution you on taking both a stroller and a car seat unless the car seat sits inside the stroller as you will have to carry both of those, unless you are checking one of them to have in California.
If you are changing planes at a terminal, I encourage you to get safety harness for all of your children so they can't wander far from you. I hate to say it, but a yound mother distracted with 4 young children is an easy target if someone happen to want to kidnap a child.
You will want to travel with the bare essentials and pack the items you need at your destination in your suitcase. Afterall, you will be able to get restocked as soon as you get your luggage at the airport. Keep the children's backpacks fun, but light so they WANT to carry them and suggest they put their favorite stuffed animal in it..it gives them extra comfort and security and if it has something they treasure in it...they will remember it as well.
I hope these tips help/ Have a safe and wondrful trip. Don't forget to pack some children's bendryl, just as soon as you leave it at home, one of you children will get motion sick from the flight! :-) Make a game out of their ears popping as the plane is taking off so they don't get scared. Lollipops are great!!