"Either God or Energy are eternal - which is it? Or what is it that is eternal?"
That's the mother of all scientific and philosophical questions, wouldn't you agree?
I think something eternal would be something absolutely true. Something eternal suggests a pinnacle of knowledge or understanding, reduced more and more to something beyond scientific inquiry. It would be a kind of knowledge unto itself that could never be wrong in any instance. Science moves in this direction. Science wants proof to demonstrate validity, and your question is a great expression of that. In the context of your question -- philosophical, with questions involving God -- I ask what your underlying assumptions are, especially since you stated your two options as essentially "God" and "Energy". Do you consider these options mutually exclusive?
Scientific inquiry in a philosophical context ("What is eternal?") is a near-perfect human question, IMO, in that it stretches both our intellect and our beliefs in the assumptions we make underlying the search for what is eternal or true. Intellect and belief work together to push scientific discovery to new places and levels. Human nature needs to sort what we see into meaningful understanding -- that is, science -- but the problem is that we as humans keep looking for and encountering and discovering new things. With telescopes and microscopes, for example, we discover more and more dimensions of "Energy", as you called it, both bigger and smaller than our grandparents ever imagined it to be.
This is not new to humankind, either. For instance, the laws of thermodynamics you quoted were first stated only about 150 years ago. In general terms, scientists developed those laws as engineers first started building engines, and discovered the principles of tranferring energy. Engines and industry transformed human life a great deal. Until then, almost all humans lived a subsistence existence, and now you and I type to each other on computers in our homes. It's no wonder that these laws of thermodynamics are now considered scientific bedrock, considering what that understanding has provided for us.
These laws are not universal in their usefulness, however. Sub-atomic physics are full of theoretical things that are inferred but not outright proven. Is this science or philosophy? Are things such as quarks and string theory valid, true (even as their proponents clearly state that there existence cannot be "proven") or are strings and quarks fanciful scientific belief? Are these things (and our understanding of them today) true and eternal?
The laws of thermodynamics are valid and true inasmuch as we understand what we see today. That does not make them eternal. Furthermore, Big Bang and evolution are perfectly useful ideas that serve a scientific purpose today that is valid for us us today. I believe in them myself. None of that makes them eternally valid either.
And what about the things we discover in the next five or ten or fifty years? Is it possible for us to understand anything true or eternal today, scientifically or not, when we clearly KNOW that we DON'T KNOW so very much scientifically? The Earth and the humans on it are much smaller today in relevance to the universe as we now know it than humans were to their world a thousand years ago, where their part of the world was essentially all that existed to them. How can we be closer to the truth of our universe if the idea of a universe is new and without limit?
I say that assumptions we make as scientific bedrock ("laws") serve a perfectly useful purpose, as long as we don't make the assumption that what we know today is perfect or unchanging, or eternal. Hubris is "excessive pride... a comparison of the self to the divine, the gods, or other higher powers". Humans are full of hubris, and throughout history we have repeatedly conviced ourselves that we understand enough to know the "truth". The human race has done this politically and scientifically and religiously over and over throughout recorded history.
Here's where "God" comes in, as I understand it. God can be understood in part as a euphemism for an order or validity of things we believe but can't see or prove. In no way do I mean to imply that there is anything invalid about these assumptions, and it's pointless to deny that the scientific world uses these assumptions every day. Gravity, a force that every child understands, defies all attempts for science to reduce it to simpler physics. We understand it when we see it, and we assume it's presence throughout the universe, but we don't know what the attractive forces are between an apple and the ground, and between the earth and the sun. God then becomes one part of the explanation of what we see -- if nothing else, a metaphor for the belief in the existence of a truth and an order and a possible understanding of what we see. This belief in God doesn't take the place of a scientific understanding, nor does it dictate the direction of scientific inquiry. God represents the the bridge between appreciating our existence in our world as people and understanding and explaining it scientifically. I believe that kind of faith is absolutely essential to all scientific progress.
You say "I have a hard time believing that every 'law of physics' that our galaxy seems to be based on were null and void before our universe and will be so once again when our universe dies." Then you ask what is eternal. I say that something truly eternal is God-like, an ultimate, unassailable truth. No human will ever shake hands with God. No scientist can ever explain everything in "eternal" terms, because we don't have minds that organize thought that way. We can't really imagine what "eternal" means, philosophically and scientifically. We see beginnings and ends, literally and metaphorically, all through our lives, and we want to apply that framework to everything else out there in the universe.
I think science works much better on a smaller scale, moving step by step in small, logical progressions. The world and the universe are uncovered slowly. Slower explanations always help me understand! If there is something eternal for us to know, scientifically or otherwise, I believe we certainly aren't capable of knowing it, but we are driven by our belief in it.