But my daytime pics are perfect - crisp and colorful. I've played around with the mode settings and ISO settings, not much difference. Any ideas/suggestions?

I have an Olympus C-5060 BTW.

Sensors in these cameras are small, and therefore are a lot noisier to begin with as the camera needs to boost the signal more which contributes to the noise you are seeing and much more apparent when trying to shoot at night.