The easiest method would be to build the noise right into the animated pieces (layers). Photoshop brush with some airbrush/noise/scatter-type settings would do it.
Animated noise is a bit more involved. You’d either have to do three versions of each piece and circulate them, or precomp an animated fractal noise layer with a soft mask to each one of them.
I’m pretty sure that a static (non-animated) noise will — aside from being the easiest — look best.