Poor Odo...he's my favorite because he's such a mystery. He mentioned his attempts to eat and drink were "messy" without elaborating, which makes me draw a few conclusions as to what happened.
A) He wasn't sure what to do past the chewing stage, so the food went everywhere. (Imagine a small child eating)
B) He did swallow it, and it just went right through him in the most literal sense. My Star Trek encyclopedia book I've had for years says he only has "an approximation of an esophagus." No stomach means the material has nowhere to go but down! (Oh boy, do the 'clothes' catch it or does it end up in a pile where he was sitting?)
C) He managed to chew and swallow, and it floated around inside for awhile until it was expelled when he reverted to his liquid state. (Poor Doctor Mora...imagine having to clean that up!)
What do YOU think happened? Be as silly as you like if you want to