Sometimes a being is depicted as a body-less mind (gas, energy or even less natural).
It seems highly doubtful a gas being could manage issues such as:
(1) Maintaining a gas cloud that neither dissipates nor gets diluted by surrounding air. (It would face the greatest active forces against it in a planetary or stellar atmosphere or magnetosphere. In "safe areas" like interstellar space, it would be most lacking in energy sources to maintain itself.
(2) Maintaining structures whose locations could be reliably accessed. (Presumably, not every molecule in the gas can contain every memory, mechanism for controlling the cloud and interacting with the world, etc., so it is necessary to locate the desired item. A gas cloud where every molecule has a permanent stationary position seems to be an oxymoron. Finding all the "moving targets" would be problematic.)
Nevertheless, we are in effect speaking of a being with a "body" which simply is not solid or liquid. Therefore, this seems the least implausible.
What an "energy being" would be is questionable. To the extent we are not talking about a "gas" and we are talking about "energy" as opposed to "matter", I would say it does not consist of protons, neutrons, electrons and similar particles. "Energy particles" would be photons, W's, gluons, gravitons, etc.
I would think it would be impractical to use photons traveling at light speed in something resembling normal space-time. To keep the photons in a closed area you would either need:
(1) A vast gravitational field to keep the photons from traveling away. This seems to limit it to being around a black hole. (Perhaps a group of neutron stars could keep photons moving around the group, but if the neutron stars were close enough to do this, I suspect the system would be unstable and collapse.) Without some other counterpoised gravitation source(s), the photons would either be:
a) Outside the event horizon, where they would escape from the area
b) Delicately balanced exactly on the event horizon
c) Inside the event horizon, where they would fall to the singularity
As I understand it, a photon at exactly the event horizon which is attempting to move outward radially from the singularity will neither escape or fall. These photons would remain on the event horizon, but presumably would not move around on the event horizon to interact with other photons. Therefore, those would not seem to make a functioning system as a group. I'm not sure whether it is possible for photons that are not trying to travel radially outward to stay balanced at the event horizon. (On the one hand, it makes sense there should be some orbital radius for objects traveling perpendicular to the radius at any given velocity. On the other hand, if "radial" photons are frozen at the event horizon, it doesn't make sense for photons with non-radial trajectories to also be balanced at the event horizon.) If this is possible, one might think that over millions of years photons would collect on the event horizon, causing it to become "full". What would happen then?
Even as an artificially designed entity; a system in which these photons could interact on a large scale (to act as a unit) and do so in a useful, structured way without particle collisions knocking parts out of their proper place, and not be disrupted by the curved space-time would be challenging.
(2) Slow the photons down far below light speed. Photons can be slowed using high-tech scientific devices. However, this means an artificial system dependent on devices made of matter, whereas we are discussing "energy beings".
As far as gravitons go, I feel my knowledge is more limited. I'm inclined to think that with the relative weakness of the gravitational force and the difficulty scientists have detecting gravity waves that this is not a promising force to work with. My impression is (correct me if I'm wrong) that gravitons are not influenced by the other forces of nature. If that is the case, it limits the ways gravitons could be controlled to act systematically.
To manipulate gravitons, I assume, would mean manipulating gravitational mass. Most often we think of this as meaning proton, neutron and electron matter as the source of the mass. Working with such matter to influence gravitons doesn't really sound like an "energy being" to me.
Energy particles have mass, even photons which have no "rest mass" have mass as long as they aren't "at rest". Perhaps it would be possible to have something influencing photons, and then the mass of the photons influencing gravitons. It sounds convoluted, but perhaps we can't exclude the possibility. Considering the complexity and other factors it does not seem likely to evolve naturally.
There is a close relationship between the force of gravity and the foundation of space-time. Perhaps it would be meaningful to treat a "graviton being" as the same as a "space-time being". There has been SF that imagined beings integrated into the "fabric of space-time". It's beyond me to comment on the scientific merits of that. While such beings would be "body-less", at least in some senses, it doesn't strike me as what people mean when they describe something as a "body-less being" or "an energy being".
W's, Gluons, etc.
When we get into W's, gluons or other particles that don't represent long-range forces, we'll be talking about the quantum realm. The W's and gluons are associated with the "nuclear forces" and may not be meaningful if we have no matter to have nuclei. At least in the contexts we have observed these kinds of particles, huge amounts of energy are required to access them. If this were also true in the case of these particles independent of "matter particles", what can we deduce? If nothing else, the high energy levels would probably make proximity to such a being deadly to an organic being.
My inclination is to believe that if these kinds of particles were in atomic nuclei, those particles in each nucleus would not be in communication with particles in another nucleus. If these particles, when in a nucleus, are only in communication with other particles in the same nucleus, then we have to ask whether there are enough such particles in a nucleus to make a functioning being.
On the other hand, if they are not in a nucleus, I believe we lack scientific evidence of such free particles to do much more than doubt whether such particles can exist freely long enough to make a functioning being.
We do know we are talking about particles that operate according to quantum physics. The probabilistic nature of the actions of these particles may make them less well suited as dependable working parts for complex beings. (Humans are made of atoms that are made of particles that follow quantum physics. However, when those particles are structured into atomic matter, the probabilistic aspect is not discernible at larger levels. Without being structured into something other than "energy particles", it may not be dependable enough.)
We could consider constituents of the universe at a scale smaller than photons, gravitons, W, gluons, etc. However, we know so little about what levels may lie between those particles and the most fundamental pieces. Once we reach the lowest level, we may very well be back to talking about whether beings can be made from the "fabric of space-time".
As far as any of the above possibilities, I don't know whether any of them fit the common images of "energy beings", which are frequently depicted as blobs or spheres of light and color.
In considering how a being might exist but not have a body in the usual sense, in the above section I commented on the possibility of a being in the "fabric of space-time". Perhaps this is a misuse of terminology like stories that refer to a being "from another dimension", which is nonsense as "a dimension" is not a place.
I would think if a being could be "of space-time", as opposed to we who are "in space-time", the being would be associated with a location in space-time rather than being able to travel from place to place. That begs the question whether the being could be associated with a location in space, but not be located at a particular "location" in time. If the being did not "move through" or "experience" time similar to how we do, could we communicate with it? If what was associated with that location in space-time did not move along the time axis, wouldn't it be static, unchanging? Wouldn't that make it more like a photograph of a being, not a living being?
Even if it were not static, how could it interact with those of us made of matter in three dimensions? It might be one thing to have a story about high-energy physicists trying to perceive superstrings / membranes discovering evidence of beings at that level. But stories suggesting such beings could express themselves in a form we would interpret as a macroscopic "body-less being" seems much more doubtful.
In considering what else the universe is made of, I realized there are also "fields". In classical physics, a field is created around something exerting a force. For instance, a magnet exerts influence around it. The area around the magnet, especially the area close enough for the influence to be significant, has the "magnetic field".
However, in quantum physics quanta are sort-of particles and sort-of waves. Electrons don't really form a solar system around the nucleus, but make up a more nebulous area. Quanta don't act like billiard balls, but have various probabilities for possible actions. In this scheme, how much is a field an effect of an object and how much is it another disguise of the underlying phenomena, as are the semblances of particle and wave? Here's another weak area in my physics understanding.
Fields are associated with forces of nature. In the macroscopic world, there are electromagnetic fields and gravitational fields. If there is a way to organize a field to be a complex system that would be distinct from organizing a complex system using photons, gravitons or such, I'm not aware of it. Perhaps a being could have a field around it, as a magnet has a field, and control the field to some degree to influence the world, but I don't see how the being could be the field.
I think the main other alternative is a supernatural being. While science cannot prove that supernatural beings are impossible, we lack scientific evidence that any do exist. Science is a study of the natural world. The supernatural is outside the scope of science, and therefore does not have much place in fiction based on science.