Modrons arise spontaneously when there is an insufficient number of modrons in the universe. In a way, they are the universe's own attempt to self-regulate the amount of disorder present in its own system.
Just as a body struggles against death, so does the universe vie against entropy. Nothing catalyzes the inevitable heat death of the universe like the use of magic.
That's what modrons say, anyway.
Modronium is like modrons: a logical extension reaching its own conclusion.
Modronium is a metal. Modrons can "vanish" part of the metal. The parts of the modronium that remain are still connected--though no metal remains between them--and will retain their weight, orientation, and rigidity.
If you make a modronium pole and vanish the middle section, you would be left with two short lengths that preserve their distance from each other and their orientation. The middle section has just been phased into a different dimension without losing any connectivity.
It's all very logical. Nothing at all to do with eldritch madness. Don't even suggest such a thing.
Examples of Modronium Objects
A modronium coin attached to a much larger, out-of-phase piece of modronium. Since the coin is attached to an extradimensional mass, the coin is very heavy.
Modronium shoes with their soles located eight feet above them. If the soles are placed on the roof of a building, a person can walk around below them, eight feet below the roof (no matter how far down the floor is.) You don't even need a floor, since you are walking below the roof, while resting your weight on it.
A modronium sword is just a grip and a sword point, that hovers three feet in front of the crossguard/basket. It still weighs the same, and handles the same, but it cannot be parried (since there is no middle part of the blade). True, you cannot slash with it, nor use it to parry a blow, but it is much easier to land a stabbing hit. [Mechanically, modronium weapons get +2 to hit, but no bonus to damage.]
Modronium has also been made into all sorts of deceptive items and tools for deception.
Modronium is not magical. It relies on a novel principle of the universe that is largely unexplored by non-modrons.