We need to break this down - and in so doing, we will see very quickly that most issues evaporate.

Orcs: these are entirely the literary invention of Tolkien. From descriptions and from his consultation with an illustrator who did some work for him, the orcs generally come across as scrawny dark creatures. But it matters little since they are not a matter of folklore - they are not mythological. How subsequent illustrators depict them is individual artistic choice, and in this, I expect there is a great deal of cross-cultural borrowings, but there are many rabbit holes to pursue with that - and I ain't doing it. Some fantasy authors of limited imagination have appropriated the poor orc, but the creature does not belong to them: the orc belongs to Tolkien. The point here is that orcs are NOT mythological.

Ogres. This word is a late, French importation into the English language. The word is often used to translate folktales from other cultures, and one finds illustrations of them for published compendiums of foreign fairy tales, but again, we're looking at artistic invention with what is likely a fair dose of artistic borrowings from various sources. In short, this process has little to do with oral tradition.

The Japanese Oni: I don't know a lot about this, but assuming it is, indeed, an indigenous part of Japanese oral tradition, that's fine, but it has nothing to do with the literary orc, and its comparison with the ogre - whatever it is - becomes rather pale.

It is surprising how impoverished early modern English was when it comes to words for monsters. It's one of the reasons why the French word "ogre" found a place in the vocabulary. Similarly, the word "troll" was imported in 1859 - that late! Now both words are indispensable to the English language. The two words fit the typical monstrous villain that one finds in British folktales - namely a brutish figure of gigantic proportion, usually identified in the oral telling of the tale with the English word "giant." The folk, however, were not likely to use words like "ogre" or "troll" because they were foreign and late introductions.

It's always a tough thing to explain or at least explore situations when we believe we see international similarities in folklore - similarities that cannot be accounted for with diffusion. We must understand that the human mind is hardwired to see patterns, so similarities have a way of leaping off the page even when things really aren't that similar. So we have to be careful to step back and say to ourselves, "I know these things seem similar, but are they really - and specifically what is similar and what is different?"

The tendency to see similarities inspires the same question on the sub - asked about once a week - which is "why so many cultures have dragons?" The problem here is a matter of limited vocabulary: just because we use the word "dragon" to describe a variety of beasts from various cultures does not mean that they are that similar nor that they are related. They almost always are unrelated and not really that similar.

All of that said, there are limits to what people can imagine and convey through their oral tradition. The 'folk" were limited by what was believable within their cultures and within the restraints of the world they knew. They tended to think of their monsters as either in human or animal form. We do not have folktales about inter-dimensional demons with hundreds of *gorblots (a word I just made up for dagger-like appendages) who slip into our world to abduct souls to be sacrificed on some otherworldly altar. Perhaps that would make a good Sci-Fi novel, but the folk would shake their heads in disbelief. And because internationally, the folk are restricted to believe in things that are tied to the believable, traditions and the entities featured in folklore do, indeed, fall into patterns. So while I caution you to question the patterns you see, I also acknowledge that some things are similar because there are only a few ways to cut a pie!

*edit to introduce the word "gorblot" to make this demon more alien to our world.

/u/itsallfolklore stated "the orc belongs to Tolkien" and while true, there is a connection with ogres.

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They started as goblins.

Tolkien's first use of the word goblins was in the 1915 poem Goblin Feet where he treated them as sprites. By 1932 he uses the word orc to indicate the same creature, and then swaps back to goblin again for The Father Christmas Letters.

The Hobbit famously uses "goblins", and even discusses the use of "orc" vs. "goblin" in the preface:

Orc is not an English word. It occurs in one or two places but is usually translated goblin (or hobgoblin for the larger kinds). Orc is the hobbit's form of the name given at that time to these creatures, and it is not connected at all with our orc, ork, applied to sea-animals of dolphin-kind.

By Lord of the Rings he had entirely switched to orcs, and mentioned in his guide to names that the name goblin is "not really suitable". He later wrote about this transition in a letter dated 18 September 1954:

Your preference of goblins to orcs involves a large question and a matter of taste, and perhaps historical pedantry on my pan. Personally I prefer Orcs (since these creatures are not 'goblins', not even the goblins of George MacDonald, which they do to some extent resemble).

MacDonald's goblins, as Tolkien admits, are the closest to his orcs; they were banished to underground caves where the plot revenge on those "upstairs".

There's a strong sense, tracking every reference, of organic change across forms. Tolkien directly states they owe "a good deal to the goblin tradition" but he poured on enough layers of lore they became their own creature, hence his insistence they are not "goblins".

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As far as the etymology of the word goes, Tolkien specifically explains the origin multiple times. In a letter dated 25 April 1954:

Orcs (the word is as far as I am concerned actually derived from Old English orc 'demon', but only because of its phonetic suitability)

In one of his appendices to The War of the Jewels:

Note. The word used in translation of Q[uenya] urko, S[indarin] orch, is Orc. But that is because of the similarity of the ancient English word orc, 'evil spirit or bogey', to the Elvish words. There is possibly no connexion between them. The English word is now generally supposed to be derived from Latin Orcus.

Orcus refers to a god of the underworld (or sometimes, the underworld itself, just like Hades can be a place or a god). This appears to be the source of the Italian orco, identical to the French ogre.

So, in a very indirect way, there is some relation between orcs and ogres. I do want to emphasize Tolkien picked "orc" based on its sound; since the actual creature was goblin-derived, it wasn't really intended to resemble an ogre other than the coincidental similarities already discussed in itsallfolklore's answer.

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Atherton, M. (2012). There and Back Again: J R R Tolkien and the Origins of The Hobbit. Bloomsbury Publishing.

Tolkien, J., Carpenter, H. (2014). The Letters of J.R.R. Tolkien. United States: Houghton Mifflin Harcourt.