Congratulations on the move! It's good to hear you're making sure everything will be secure for the ride over.
The first thing to consider is lodging. Obviously, you can't all sleep in the car, so be sure to find a hotel where pets are allowed or perhaps rent some form of a camper if you'd like to go that route so you can stay with the birds at all times. It's important not to keep them unattended at any time.
Shane is correct that for traveling, you should be sure it is fully secure where it will not have any danger of falling, tipping over, or hitting objects in front after sudden braking.
Prior to the trip, it's best to only have one perch in the cage so that it's not so cluttered, greatly reducing the risks of getting injured if they get scared or fall off their perch. Many people prefer a rope perch as it bounces a bit with the car and is easier for them to hold on to sometimes.
Also, only leave one or two toys in that don't have bells or hard components. Soft sisal or palm toys are good, as are very light wicker balls or kabobs.
As for food and water, leave only a little bit of water in the bowl during travel, or use a water bottle. If they aren't used to drinking from a birdie water bottle (the same ones used for rodents), then you can introduce on a few weeks before hand so they're used to it. Food is generally fine to leave out, not too much, however. You'll have to be sure to check food and water at all stops made.
Consistent car temperature is a must, and many budgies are soothed by soft music playing. If they seem very agitated, covering their cage will help them to relax.
Finally, if possible, take as many back roads as you can. Highways are fast, but they have a higher risk of accidents and the obvious increase in traffic, which oftentimes is present in the horrible fumes that can be taken in by the air conditioning system. If there is a lot of traffic, put your car on the "recycle air" setting so that it re-circulates the cabin air and eliminates potential hazardous fumes from the car in front.
That's just about it, I think
I hope the trip goes well!