I'm going on a road trip. How do I check all the fluids in my 2004 Toyota Corolla (oil, trans, brake, power steering, antifreeze, windshield washer) as well as tire pressure?

Why do you need an 'overhaul' on a 2004 Corolla? Please define that, a 10 year Corolla unless you have racked up 250,000 miles at least is not half way to it's expected lifespan. Check the oil, simply pull the dipstick and look, pop the radiator cap COLD and top off, and as far as tires if they are worn out then ...oh well...there is no way in heck to predict a flat tire...relax...your Corolla will drive you to Vegas to "frisco and back 20X

If you haven't had the car serviced in 1 year I would take it into the dealer a and see what they recommend for a"one year check up." I certainly have them check the oil as it must be sludge by now. Have them do an alignment and check the tires for cracks and possibly being out of date as there was a big flap about that a while back. Also having the tires rotated would be a good idea. I don't know how many miles you have on it, but have them do that service and tell them it hasn't been serviced in a year. Have a good trip!