A couple of things. Others are right that you don't need to register with a CHP. However, if you did have to register, the guns must be taken in person to OPD headquarters downtown. They limit you to 2 or 3 per visit. A rather ridiculous policy. Years ago, I had to take a new gun I bought out of town to the OPD to register. Another guy was registering a 3rd gen S&W that OPD confiscated because he had a firearms related infraction on his record (discharge in the city when he was younger). Ironically, the sheriff had issued him a purchase certificate.
Possession is what matters with the registration, not purchase. If you buy a gun outside Omaha and want to possess it in Omaha, you still have to register it. If you buy from an FFL in Omaha, they will give you a registration card to take to OPD. If you buy it outside of Omaha or in a private sale, you have to take the gun to OPD.
Also, I'm not sure where the FFL comes into play. If you own the guns and they are located elsewhere, I believe you can ship them to yourself at your new address in Nebraska. You can also bring them yourself when you move.