It can be measured to quite a large number of significant figures. So yes, we have good operational definitions.

Edit: We can tell you how much of it there is. But if asked about its "location" or its "velocity", we have to frown and say "what are you talking about?"

To me it is the quantity that makes the world un-exploitable. For example, It can be kinetic energy so it better stay constant in a closed system. Luckily we found this quantity and used it. It is not an object or anything. It is a mere beautiful idea and concept.

I think the crux of the OP surrounds the definition of Energy.

My own background is in Mechanical Engineering so for me I use the idea of Energy to work out how thinig do or dont deform, how things move or how to make them move in a prticular way, that kind of thing. So I know how to use the concept of Energy but reading through this thread it occured to me, I couldn't give a clear definition that didn't end up sounding really hand wavey & vague.

Indeed. I think of energy as describing something about the overall configuration of a system. The details about what that something is is usually not needed. If I'm using a laser and a CNC machine to cut through metal sheets, I don't care about exactly which atoms get excited and what happens to them. I only care about the larger-scale results, namely the thickness that the laser will cut through, which can be predicted using energy equations.

I find it extremely interesting that energy equations can be used for both large-scale and small-scale applications. Properties of everything from subatomic particles to planetary systems (and larger scales) can be predicted using energy equations.

Maybe....not sure why you criticized us for not answering before posing the question, but anyway...

I think people have more trouble with the definition of energy than they should. Yes, the dictionary definition is broad/vague, but that's just because there are a lot of different types of energy and it is tough to tie them all together into one definition. I suspect though if people put the same amount of thought into the definition of "car", they'd realize it has similar issues of specificity that don't bother them.

So how do we get past this? By defining all the different types of energy separately and then just tying them together loosely with the standard definition or conservation of energy/Noether's theorem. Take kinetic energy: Kinetic energy is energy due to motion as defined by KE=.5mv^{2} It's simple and defined precisely via the equation. It's much more straightforward than the definition of energy itself. And:

I think it it should be enough that it is a useful mathematical relation between certain properties/parts of a system. "KE" is a mathematical relation that was discovered and is useful and is mathematically equal to the other mathematical relations that we therefore bundle together under the header "energy". It doesn't need to be an object (other than a mathematical object) and doesn't need to reside anywhere specific in order to be real (similarly: where is your speed? heck: where is your money?).

I think energy is not just a concept, it is a feature of the nature of the world. That the world has a nature one may argue but assuming it does, then energy is a feature of it. If you take all possible worlds you can restrict them by using laws. All those possible worlds that don't follow a give law you eliminate. There are possible physical worlds like ours in all ways except that they do not allow one to define energy as we do. Our world does. The fact that it does is not the concept of energy - it is the fact of it. What fact? There are many but suffice to say our world does not allow interactions between physical entities that do not conserve a certain quantity within certain probabilities and for certain times. This is true using the classic, quantum mechanical, and relativistic notions of energy. Even if you do not admit that the world has a nature you will still admit that the concept of energy is more than just a concept because it constrains the type of your sensory experiencing.

You can have the concept of energy and live in a world where its definition does not apply. We live in a world where it does apply. Its not just an idea.

I doubt that the concept of energy would have been created in a universe in which it does not apply. We created it solely because it is a useful concept that greatly simplifies certain physical problems and can, in some cases, offer an explanation solely in terms of itself.

On the question of whether energy "really exists" or not, I neither know nor care. Neither possibility changes physics in any way.

I think this question is interesting, but needs refinement. Imagine a scalar field where at each point energy is measured. I assume the question is whether such a field can be space independent over a certain neighborhood...I mean I know this is true for zero point energy in a vacuum and certain QFT systems.