If you're planning on stopping for even a cup of coffee the best thing to do is to have a NR permit for every state you'll be stopping in.
If you're traveling through without stopping the you'll be covered by the Firearm Owners Protection act of 1986 ( Just "Google" McClure-Volkmer Act.) but any firearms you have must be cased, unloaded and stored - separately from the ammo - while you are traveling through.
Iffin' I omitted anything I'm sure there'll be a team of experts along shortly...
Good luck with yer trip !