"It is always legal to transport your firearm in your trunk, Unloaded and cased. In vehicles without a trunk, the firearm must be in a locked, hard case. (Federal Law)"
I meant it to be a catch all, if you aren't sure if what you're doing is legal, carry it like this and you'll be fine. I am still pretty sure there are no laws at least on state statutes that are more restrictive, other than the loaded shotgun thing. Also omaha's open carry permit still applies to openly carried firearms, and NE CHP applies to concealed, concealable firearms. I don't know of any law that prohibits carrying a loaded rifle, within reach, while driving (or riding) however a hunting guy may be able to pipe in if there is such a thing. Honestly if you feel you need to drive (or walk) around with a loaded rifle ready to rock, well you are more paranoid than me, but I still think it's legal. Not that you'll do it for long flashing it around without getting at least questioned about it by some "authorities".