So we know that Odo has no respiratory system or digestion system, but given this how it that has a voice box and can speak? Are we suppose to assume that he designed (for lack of a better word) his humanoid form to have a voice box? Wouldn't that be too hard for him to form, or did he do it despite difficulty out of necessity?
Just because he doesn't have a functional respiratory or digestive system (in the sense that such things are normally used for introducing air and nutrients into one's circulatory system), doesn't mean he can't simulate the ability to breathe (or speak, for that matter) through use of a simple air bladder, wind pipe, and "vibrating membrane" (as @Xantec puts it).
I think I read somewhere that Odo only has an approximation of an esophagus. As for speaking and imitating breathing, it isn't outside the realm of possibility that he can formulate something like lungs and a vocal tract. He does have a rough sounding voice(thanks to Rene Auberjonois being awesome) which tells me that maybe his 'vocal cords' were never quite right, just like he had trouble with his face. :)
This was addressed in the DS9 novel "Fallen Heroes". In short, Odo has learned to function himself a functioning voicebox and vocal cords using his shapeshifting skills.
"Now what?" asked the Ferengi. Quark had donned another coat in his office, looked even dandier than usual, inappropriate garb for such a sombre occasion.
"There are other ramps, said Odo, his voice warbling as his vocal cords reformed, shifted. "But they are in parts of the Promenade that are blocked' He thought for a moment. “I believe I know how to proceed.
He turned, scanned the blue-flickering scene for a turbolift door. It was aid to tell exactly where he was in the desolation; everything looked so different. He spotted one, led them over.