Is it possible to model the Universe in an object oriented manner from the subatomic level upwards?

If what you mean by "the Universe," is the entire actual universe, the answer to "Is it possible?" is a resounding "Hell no!!!"

Consider a single mole of H₂O, good old water. By definition a mole contains ~6*10²³ atoms, and knowing the atomic weights involved yields the mass. The density of water is well known. Pulling all the pieces together, we end up with 1 mole is about 18 mL of water. To put that in perspective, the cough syrup dose cup in my medicine cabinet is 20mL. If you could represent the state of each atom using a single byte—I doubt it!—you'd require 10¹¹ terabytes of storage just to represent a snapshot of that mass, and you'd need to update that volume of data every delta-t for the duration you wish to simulate. Additionally, the number of 2-way interactions between N entities grows as O(N²), i.e., on the order of 10⁴⁶ calculations would be involved, again at every delta-t. To put that into perspective, if you had access to the world's fastest current distributed computer with exaflop capability, it would take you O(10²⁸) seconds (on the order of 10²⁰ years) to perform the calculations for a single simulated delta-t update! You might be able to improve that by playing games with locality, but given the speed of light and the small distances involved you'd have to make a convincing case that heat transfer via thermal radiation couldn't cause state-altering interactions between any pair of atoms within the volume. To sum it up, the storage and calculation requirements are both infeasible for as little as a single mole of mass.

I know from a conversation at a conference a couple of years ago that there are some advanced physics labs that have worked on this approach to get an idea of what happens with a few thousand atoms. However, I can't give specific references since I haven't seen the papers and only heard about it over a beer.