If you are driving yourself cross country, crates are your best bet. Look on craigslist and the local buynsell/thrifty nickel for them now so you do not have to pay full price. If you put them in the plastic carriers, like a VariKennel 400, three large birds or 4 small ones will fit comfortably. For this size, I usually can find them for $35. Garage sales are another great place to look, and you have time which is great. You want to make sure they can stretch out like birds do when they get hot or sun bathe.
Since you are moving in the summer, I would suggest an open trailer and cover the back of the trailer across the top of the crates with reflective (like moonblanket) material. A little cross ventilation is good, and many of the Uhaul or DIY trailer kits you can buy at Home depot, have solid sides with a 6-8-in rail at the top, which is perfect for strapping the reflective cover to. I suggest NOT using shavings, as they will blow around, but two things work well, sheets of newspaper and the disposable bed liners (look like giant diapers). Change them am and pm, and if the birds are not over crowded, they will not get too messy. Another good solution, albeit a bit more expensive are the excelsior nesting pads (eggcartons.com) they pull moisture and give traction too.
Feed dishes are as simple as one of the bigger cans used for tomatoes or pumpkin (26oz?) with a couple of holes drilled towards the top and zip-tied to the door. For distance I prefer these deeper cans, as the birds can fit their entire head in easily and they are a bit deeper so the water doesnt slosh so much.
Nature's Miracle works good for odor and spot cleanups (ie poopy feet n tushes). Another good enzyme based deodorizer can be purchased at Jeffers Livestock (online) and is called Barn Odor Destroyer. Works wonders around the coop too. It is a concentrate, and less expensive than Natures Miracle.
A great thing about pulling a trailer is that you can carry 10 gallons of water, plenty of feed and their "gear" all together. If you stay at hotels, you will probably need to towel any crates carrying roosters so they do not wake anyone up. If you hit really hot weather, you may need to make an adjustment and drive at night, and sleep during the day.
I worked for the government for 10 years and moved to 7 states (5 yrs in Alaska), so if there is one thing I am pretty good at, its moving and packing for our furry and feathered family members! Wish you the best, and if you have any specific questions, just email or pm.
