I've only moved cats/dogs during a short 5 hour relocation, but my suggestions would be:
Feed--bring in your vehicle(s) in a sealable tub or container. Appropriate greens & veggies, pre-chopped and in sealable containers to last the entire trip. Maybe some scratch grains.
Water--bring in jugs and have some type of cup or waterer available for birds to use during the trip
Bedding-shavings/hay or your choice; also have inside the vehicle, handy
Poop scooper/disposable bags for cleaning
Large sized pet carriers are nice because they are ventilated but also provide security/privacy to birds. Spend the money up front on what you need--you can always re-sell/donate carriers later if needed. Only put birds together who you feel will cooperate with each other. Don't overcrowd the carrier/cage.
If you are moving soon (cold weather), I would not transport animals in the bed of a truck or on a trailer. Too cold, too much road noise/stress, can't be monitored properly. I've often thought that if I had to move lots of critters, I'd rent the biggest SUV or van I could, pull out the seats (if possible), and hopefully have ample space for carriers, etc. in a climate-controlled environment.
Will you be stopping overnight or driving straight through? Plan ahead and locate pet-friendly accommodations so your birds won't have to spend the night in a freezing vehicle in the parking lot. Maybe even check with folks here at BYC for B&B's, hotels, etc. along the route you plan to take, in case someone has suggestions/recommendations. Even "horse hotels" might be an option, if an enclosed, secure barn is available to house birds overnight and if the situation looks secure enough from foot traffic/predators/other farm critters.
Load your critters at the very last, just before you head out. Make sure everything is in place and that if more than one vehicle is being driven, you both have cell phones charged, phone numbers available, and a travel plan.
How are things set up at your new home? Do you have a ready, secure location to move the birds into once you arrive? No fun to be scrambling after a long trip to figure out where everyone will go, when under stress anyway.
I'm certain you've already considered all these suggestions, but IMHO, one can't be too prepared. Best of luck at your new home!