move, shift on one side
挪 centers on shifting something from its current place: moving it, or sliding it to one side. The idea is physical displacement rather than abstract change.
挪 combines 扌 (hand) with 那, which likely contributes the sound. The hand radical suggests moving or shifting by hand.
A hand 扌 beside 那: picture a hand nudging something to the side, shifting it out of the way.
For ダ, imagine a hand moving a heavy object with a dull thud: the sound 'duh' cues ダ as the object shifts to one side.