Many characters are referred to, both in canon, and by the community, as being 'powerful'.
Gandalf is a powerful wizard; Sauron is very powerful; Morgoth is one of the most powerful beings to have existed.
What makes an ordinary human 'powerless', relative to a Maia or Vala, etc.?
Is there an in-universe explanation of the differences in power between beings and what makes someone powerful in the first place?
The relative strength or ability of the different beings seems first to be based on their nature. That is, a Vala is greater than a Maia, who is greater than an Elf/Man/Dwarf/Hobbit. Within these types of being, there is wide variance in strength. Sauron, for example, is among the mightiest of the Maiar, while Gandalf would be (at least at first) among the weaker. This where the second way of looking at strength comes into play. In the text, there are many references strength from the will. Fëanor's fiery spirit, for example, or Aragorn's mastery of the Palantir.
So, I'd say that type rules first. For example, Fingolfin, among the greatest of elves, is no match for Morgoth. (And this is why the Noldor had no hope of defeating Morgoth in the long run; a Vala, even a fallen one, is that much stronger). After type is accounted for, then differences in individual strength/will are at play.
The Maiar seem to be another matter. Gandalf and Sauron are Maia, as are Balrogs. But the Maiar may be less in strength than Elves or Men. I hesitate here, because the classic example might be Gandalf matched against the Witch King. The Witch King is a Man, but one given much of the power of a mighty Maia (his master Sauron). There's no guess how that might have ended. Examples from the Silmarillion might be Glorfindel of Gondolin against the Balrog, or Beren and Lúthien against Sauron. Neither a perfect example, but the possibility is shown that an Elf or Man may challenge one of the Maiar. An Elf is not by default mightier than a Man, except that Elves are not subject to old age or illness as Men are.
To your original point, the question of why a Vala or a Maia is more powerful than an Elf or a Man, I think the main distinction is that of those that existed before the world, the servants of Ilúvatar, and the Children of Ilúvatar (Elves and Men, though we can include Dwarves - created by Aulë - and Hobbits). The pre-creation beings are mightier than the created beings. As for why, I suppose it's one of those things that simply is assumed without much explanation.
I hope that's helpful!
My understanding is that the relative power of different beings in Middle-earth is determined largely by what they can and can't do. I think a ranking of the inhabitants of Middle-earth (or, more correctly, of Ëa), in order of their respective amounts of power, from most to least powerful, would look like this:
Eru Ilúvatar: The most powerful being of all. The made the universe (Ëa) and he made life. Only he can truly create life, and although Aulë made the Dwarves, they were allowed to exist only by the grace of Eru. Powers unlimited, obviously immortal.
The Valar: Melkor (also known as Morgoth) is the most powerful of these, although Ulmo, Mandos, and Manwë are nothing to sneeze at either. The Valar are described as creating mountains, stars, rivers, canyons, forests, oceans, lakes, and so on. Everything in Arda is subject to their will, but (aside from the fallen Vala Morgoth) their will is not their own - it is a reflection of the will of Eru. Immortal. Powers virtually unlimited.
The Maiar: Sauron may be one of the most powerful Maia, but it is difficult to say so with any certainty. Melian guarded kingdom of Doriath from the evil of Morgoth for thousands of years. Ossë, a vassal of Ulmo, is described as sometimes going against the wishes of his master, and can only be calmed by his wife Uinen. The Istari are obviously Maiar as well, and of these, Olórin (i.e., Gandalf) is the wisest and most powerful. Whereas the only Vala to fall from grace was Morgoth, it is suggested that many of the Maiar were led astray by him, including Sauron, Ungoliant, and the Balrogs. Immortal.
Miscellaneous beings: Shelob (a descendant of Ungoliant), Tom Bombadil, Goldberry, the Dragons, Ents, Stone Giants, etc. Origins and powers largely unknown and undescribed.
The Eldar (Elves): Much more powerful than Men, but far less impressive in comparison to the Valar and Maiar. They are wise, and many of them are talented in the use of magic; they are also great craftsmen. They seem to "build" and "preserve" rather than "create"; they can build great fortresses and palaces, but they couldn't, for example, make a mountain appear out of nowhere, as the Valar can. More or less immortal.
Dwarves: Almost incorruptible; resistant to domination. Great craftsmen. Again, they build and improve things rather than "creating" them. Extremely long-lived, but not immortal (although they are very hard to kill).
Men of Númenóreans and the Dúnedain: Men, but better. Compared to normal humans, they are wiser, more powerful, longer lived, more skilled with magic. Great craftsmen, although their skills have waned in the years after the Fall of Númenor. Most of them are less easily corrupted than normal humans, but still corruptible. Builders, not creators. Long-lived, but not immortal.
Hobbits: Related to Men. Little or no magical ability, small and unimpressive, quaint and rustic. Incredibly resilient and resistant to domination and corruption. More likely than other races of Men to be friendly towards the Elves. They don't create, and they rarely build anything. Longer lived than normal Men, but not as long lived as Númenóreans, Dúnedain, or Dwarves.
Men (Normal): Weak, stupid, easily corrupted. Mostly afraid of magic and anyone who uses it. Mediocre craftsmen. Die almost as soon as we are born. Strong tendency to be misled by evil overlords, such as Sauron, Morgoth, Hitler, etc. Builders, not creators. We suck.
Melkor/Morgoth was the MOST powerful being ever in Arda and Sauron was his greatest servant.
Illuvatar spoke...'Mighty are the Ainur, and mightiest among them is Melkor.' [Ainulindalë]
Among those of his servants that have names the greatest was that spirit whom the Eldar called Sauron, or Gorthar the Cruel. [Valaquenta]
Each group has its own innate abilities. The Elves have greater control over their bodies and are therefore harder to kill and are more enduring of hurts than Men. The Ainur may take on physical form but they'd have as great a prowess as any Elf physcially.
In Morgoth's Ring when speaking about reading the minds of others a note says "all rational minds/spirits deriving direct from Eru are 'equal' - in order and status - though not necessarily 'coeval' or of like original power." Every spirit is equal but not necessarily in innate power. I liken it to people being equal under the law, but of varying abilities.
It is also said that the Ainur themselves "become more impotent" as the shape of things in Arda become more defined [Morgoth's Ring; Myths Transformed]. This will occur even with men when "they have completed their function". The Ainu are spirits, but the Elves and Men also have spirits living by a union of spirit/body. In Athrabeth Finrod ah Andreth it's said "the fëar were not spirits of a wholly different kind to the Ainur".
The Ainur would be greater in innate powers than Men because that's how they were made. Elves have taken out Maiar (Ecthelion/Glorfindel/Gil-galad) but as far as I know this would be beyond Men and yet there are Men who have beat Elves. I should point out that Gil-galad and Elendil both took out Sauron, a weakened Sauron, a Maia nevertheless. In that instance even a Man was able to take out a Maia. In Aman it appears that even Feanor was able to use his voice to overpower a Maia messenger:
In that hour the voice of Feanor grew so great and so potent that even the herald of the Valar bowed before him as one full-answered, and departed; [Of the Flight of the Noldor]
This is a power that reminds me of Saruman himself.
There seem to be discrepancies where you'd think Elves having more innate power should always be able to beat a man, but this is not always the case, or a Maia should always be able to overcome an Elf or a Man but this is not always the case. Feanor, however, was not normal and quite mighty. Weapons might simply mitigate these innate power differences between people. As seen with Fingolfin in his battle with Melkor. Yes Morgoth was weaker than he used to be, but he was quite a beast in terms of innate powers. Yet, Luthien overcame him, part Maia though she was, and she also put to sleep most of his other Maiar servants, but Sauron nearly took her out on his own before Huan saved her.
