Basically it seems that all the "conserved" properties of the universe net out to zero.
Conservation laws are misleading. The popular conception of such laws is an outdated notion from 18th and (to a lesser extent) 19th century physics. In modern physics, conservation laws are generally imposed
a priori. That is, physical theories are tweaked, fiddled with, and altered until various properties are conserved. This becomes especially clear with energy when one realizes that no one really knows what it is that is conserved because for over a century it has been realized that energy in physics isn't consistently or even well defined:
"no general, quantitative definition of energy which covers all its aspects is currently known. The lack of such a general definition was explicitly acknowledged as far back as 1902...
It may or may not be impossible to find a general definition of energy but, as we do not currently have one, we shall draw on the well-known and accepted concept of energy that uses particular examples in order to illustrate itself...
In regard to the conservation of energy, this is either postulated as a law or derived as a theorem from a set of axioms depending on the area of physics involved."
(emphasis added)
Riggs, P. J. (2009).
Quantum Causality: Conceptual Issues in the Causal Theory of Quantum Mechanics (
Studies in History and Philosophy of Science Vol. 21). Springer.
In other words, even if we could identify what "energy" is in physics generally, to the extent it is conserved it is because we force physical theories to conserve it either directly (i.e., "postulated as a law"), or indirectly by deriving it from other postulations taken axiomatically. This is not unlike the role of symmetry in physics.
There are a number of them, the best known...
Whatever the best known is, the most important is almost certainly information. It is the only "thing" that can be equally well-defined in any field of physics.
being mass/energy, electric charge, momentum and angular momentum
I can't address these all in a single post, but as for momentum:
Mansuripur, M. (2012). Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation.
Physical review letters,
108(19), 193901.
It is fairly easy to see that electric charge nets to zero, because it does so short range.
Novikov, V. A. (2016).
CPT breaking and electric charge non-conservation. In
Journal of Physics: Conference Series (Vol. 675, No. 1, p. 012007). IOP Publishing.
Dolgov, A. D., & Novikov, V. A. (2012). CPT, Lorentz invariance, mass differences, and charge non-conservation.
JETP letters,
95(11), 594-597.
(I couldn't find a free copy of the paper other than an arxiv preprint, so I've attached the real paper; it's rather technical, so if you want a one-sentence headline see the conclusion: "Moreover, in such theories charge and energy conservation seem to be broken as well.")
And as an illustration as to how conservation laws are often forced by theory to be true, we can see how we make conservation laws hold, here is the derivation of a "modified" electric charge conservation in a relativistic quantum theory in which the charge itself can vary?
Calcagni, G., Magueijo, J., & Fernández, D. R. (2014). Varying electric charge in multiscale spacetimes.
Physical Review D,
89(2), 024021.
(once again, I've attached the paper)