Is there anything that is constant under all (and not a very specific set of) theoretical conditions?

Good question. There are in fact twenty some constants of nature. Their values are invariant over the universe (if you believe in super symmetry).

Among these constants are included: the speed of light, Plank's Constant, the universal gravity constant (G), the fine structure constant( alpha), pi, and a host of others. We have no clue why they have the values they have. But we do know that, together, they form the bases for all...all...laws of physics in our universe. Change the value of one just a tad, and the laws of physics would no longer be the same as we know them.

For more on the constant of nature I recommend you read "The Cosmic Landscape" by L. Susskind, entertaining and informative reading.

Speed of light in vacuum(c) (i.e. 3*10^8 m/s)

Value of Universal Gravitational constant(G)

The above mentioned remain constant.

The first law of thermodynamics, or energy conservation, is constant in most cases, and always gives useful information. It forms the basis of many physical sciences.