Let me just give you a flavor of what Aristotlean theory of matter was like. You should keep in mind that the kinds of questions this theory was trying to answer were not the kinds of questions we tend to think are important when we think about modern (20th century) atomism. Thinking of this as "physics" is sort of the wrong framework in general; the branch of scientific thought that was most concerned with questions of matter was chemistry (physics, prior to the late 19th century, was mostly about larger things — think mechanics and dynamics, not particles).

Anyway, here is goes. In an Aristotlean worldview (and mind you, there were many variants of this, depending on what place and time you are talking about, so this is just an overview), there is what could be thought of as a base matter. This is just the "stuff" of matter. All matter is some kind of common material. This common material is infinitely divisible: it doesn't have a smallest-possible unit. You could keep chopping it in half forever if you had a sufficiently fine knife.

This base "stuff" can have different qualities to it, which determine how it behaves in the world. So if it has the qualities of hot and wet, it is air, and has a natural motion that takes it up. If it is hot and dry, it is fire, and also moves up. If it is cold and dry, it is earth, and its natural motion is down. If it is cold and wet, it is water, and its natural motion is down.

Nearly every substance you would encounter in day-to-day life is going to be some composite of these elements and quantities, which explains why not everything neatly fits into these four simple categories.

That's the basics of it. Again, this is not really a system of physics. There are separate Aristotlean approaches to physics (which are similarly unusual; there is no concept of inertia, for example), and the only "physics"-like thing here are the natural motions, which explains why some substances rise and some fall and why, for example, rocks sink to the bottom of pools of water. Aristotle's approach is all about trying to understand the natural order of things, and how that natural order might be disturbed (things with souls can disturb the order, hence "unnatural motion" is permitted — note that plants can have souls, because they move upwards). Aristotle's theories were not created to answer the kinds of questions we would put to them (and were modeled on different phenomena than classical physics was — Aristotle's physics is about the motion and growth of biological things, more than it is about pendulums and balls rolling down inclined planes, for example; he would think of "a body moving through the air" as being more like a bird than a cannonball). So "what did they think would we see if we looked through an extremely powerful microscope at an atomless world" is not a question they would have spent any time thinking about, because they didn't have microscopes (but the answer would be, probably, "you'd see more of that base matter").

If you really want to get into how different non-atomic theories worked out, check out William Newman's Atoms and Alchemy. It's mostly centered on the medieval and early modern periods, but it gives you a LOT of detail on how they saw the chemical/alchemical world. The trick of all of this is NOT to go in asking, "how would they use their system to answer our questions?" The answer is: poorly, because their system was designed to answer different questions. Similarly if you try to use our present system to answer their questions, you get nonsense sorts of answers ("what does quantum mechanics tell you about why acorns turn into trees?" is an example of how incoherent this would be).