Is there an edible, colour-less, taste-less, odour-less, water-soluble, cheaply-producable gel, solid or other substance? Suppose, for example, that some oatmeal is fixed in gel, or some other substance. A portion of the substance-with-oatmeal is then removed and added to cold milk or some similar dairy product, where it quickly dissolves, yielding a standard bowl of milk and oatmeal. Is there such a substance?

Ideally, the substance should be unobtrusive to the eating experience. This also means that it should not dilute the milk significantly. Otherwise, some taste, colour or odour may be permissible, provided it does not clash with the taste of the meal.

The substance should also not soak the oatmeal, which is why it may not be a liquid.
Are you talking about maltodextrin? It's a solid powder assembled from glucose units with no taste smell or color. It's commonly used as a carrier; it's used to dilute the actual sweet -flavored molecule in Splenda. 

If you're dealing with Hot oatmeal, you could add methyl cellulose to gel it up. Upon mixing with cold milk it will melt, acting like reverse jello; solid when hot and liquid when cold. 

You asked a rather strange question, I'd recommend instant oatmeal to prevent a possibility of bacterial/fungus growth when storing oatmeal for extended periods of time.