Orcs, in the modern sense, are, of course, the invention of J.R.R. Tolkien. He borrowed the word from Old English, in which it's usually translated as "monster", and is possibly just a less common alternative word for "ogre". But it was Tolkien who introduced the concept of the orc as an evil race of humanoid beings, from which Gygax obviously took his inspiration when writing D&D. Tolkien's orcs are the result of twisted experiments on elves, and are typically described as sallow-skinned and misshapen, although there does seem to be some variation among them. They exist primarily as the foot-soldiers of more powerful evil entities.
Physically, 1E orcs resemble resemble humans with the heads of pigs, including a long snout, prominent ears, and distinct tusks. They have brownish skin, often with a greenish tint and bristly hair (or none at all, judging from the picture). They typically wear reinforced leather, carry wooden shields and use a variety of weapons, with axes being the most common. A significant proportion of them, perhaps as many as one in six, are two to three times tougher than the regular sort, acting as leaders and their bodyguards. Like Tolkien's orcs, they are nocturnal or subterranean, and have difficulty fighting in bright sunlight.
They are described as "lawful evil". The latter half of that designation is justified by, among other things, a love of torture and a habit of eating humans. The "lawful" designator implies a hierarchical society, something that's supported by their regular use of slaves, and what seem to be reasonably well-organised tribes that number a little over 400 on average (including infants). Female orcs, out-numbered two-to-one by the males, are used solely as chattel and breeding stock, and are essentially incapable of fighting. All of this seems to be at least consistent with Tolkien's limited descriptions of orcish culture, and is clearly based on it.
Orcs are said to be slightly less intelligent than humans, despite which, they are all apparently fluent in five different languages, including their own. We don't know such things as how their physical strength compares with that of humans, although they are about the same size (Tolkein's orcs are shorter, and hunched with it) so there may not be much difference.
Their skin is now a sallow grey-green, instead of brown, the start of a trend that will see them become bright green in many non-D&D properties. We're specifically told that they don't look like pigs, in an obvious attempt to distance the 2E version from its predecessor, which somebody presumably thought was a bit silly. They do, however, retain a noticeable snout, complete with tusks, and have a sloping forehead with "wolf-like" ears. Unlike the earlier version, they are also habitually hunched over, although they would be still be human-sized if they could stand up properly.
Since the publication of 1E twelve years prior, various supplementary sources had expanded on orcs and their society, and some of this worked its way into the base description in 2E. Some notable expansions on the original description include a tendency to rebel against their masters, weakening their "lawful" descriptor, although perhaps not by much, since their communities can now sometimes reach populations of several thousand. A small number of them also have the capability to use limited magic, putting them on more of a par with humans in a world where combat magic seems to be very common. Their original special enmity for elves has expanded to include dwarves as well.
In other respects, they are slightly toned down. For instance, they do still eat the flesh of humans, but only as a last resort, much preferring regular meat. Their love of torture and (implicitly) rape is no longer mentioned, perhaps in an attempt to make the game seem more kid-friendly. They do, however, remain able to speak five different languages as standard, although it's now clarified that they're not actually very good at most of them.
In terms of their gender relations, they do now have something resembling marriage, although quite what this means is unclear; it may be that it could be more accurately described as servile concubinage. Certainly, the females remain incapable of meaningful combat; it's unclear whether they are still outnumbered by the males.
Differences in the rules editions means that we can now compare orcs with humans across a wider range of parameters. Compared with the earlier version, these have a slightly lower intelligence, and the great majority of orcs no longer speak multiple languages. But we can also see, which we couldn't previously, that they are much physically stronger than humans, which has some effect on their combat prowess. Proportionately speaking, their leaders are much tougher than they were before, being able to take advantage of regular character classes, and typically reaching a much higher level. This is partly due to a general inflation in character ability in 3E, but also allows orcs to remain as effective foes for longer as characters level up.
Orcish culture, with its emphasis on perpetual conflict and territorial expansion, remains much the same as before, but they are now classed as "chaotic evil", implying a lack of organisation that seems somewhat at odds with their ability to form large, at least vaguely functional, communities. Females and males are now equally common, but, uniquely among the five "evil tribal humanoid" cultures, males remain exclusively dominant, with the females as non-combatant slaves only (likely using the "commoner" character class, although this isn't stated).
PathfinderBeing a close variant of 3E, Pathfinder does not significantly change the statistics of orcs, although, in line with its increase in the range of abilities that everything possesses, they do gain the ability to fight on after sustaining injury that would otherwise knock them out. Pathfinder orcs do, however, have explicitly green, rather than grey-green, skin, and are heavier than humans of the same height. The text description emphasises their evil side, making them lazy and unreliable, brutalising their own kind when they can get away with it, and regularly inflicting torture and "humiliating physical violation" on their defeated foes. Females remain weaker than males, and are consequently used as punching bags; presumably, they're not effective in combat.
So, no, not very nice.
5ESkipping over 4E, 5E sees further rules changes, perhaps the most significant of which for orcs is the general hit point inflation that sees them, for the first time, given two hit dice instead of just the one. Overcome with bloodlust, they can also sprint towards their enemies more rapidly than other humanoids can.
The hierarchical scheme of evil tribal humanoids seen in 1E began to weaken in 3E, but here breaks down completely, with the linear progression gone, and orcs becoming one of the tougher such races, rather than the median one. This is reflected in the fact that orcs remain only slightly taller than humans, but are now much heavier and more muscular. In terms of their base statistics, they are now even stronger than in 3E, more agile than humans, by far the most physically resilient of the tribal humanoids, and have the highest scores in their mental stats - apart from intelligence itself, which has dropped a further point. Despite which, they are once again fully bilingual, although the multiple languages of the earliest editions have now gone.
In terms of their physical appearance, their face has become flatter, and their nose the most human-like yet, although they have large tusks, an elongated jaw and skin that has now fully evolved to a solid grey colour. Compared with the previous versions, they have lost their fear of bright sunlight, making them a more formidable foe even if humans can choose the timing and location of a battle. Their favoured weapon has reverted to being an axe.
Culturally, orcs have lost their desire for territory, becoming a rampaging horde that consistently moves on and rarely establishes any kind of base for long. Although numbers are never mentioned, this presumably rules out the orcish cities mentioned in 2E, and perhaps fits better with their "chaotic" designator, with everything in a constant state of violent flux. The eating of their foes is not mentioned at all, and nor is the taking of slaves for forced labour or torture; in fact, the most brutal thing they're described as doing is hacking off a dead foe's head. Not particularly pleasant, to be sure, but not beyond what you'd imagine some human warriors doing.
For the first time, females aren't mentioned at all, with the implication being that they're just as strong (and numerous) as the males, and, given the violence-is-all nature of their society, treated as equals at last.
The overall trend then, has been for D&D orcs to evolve from an attempt at emulating Tolkien (limited by the nature of the game system) to becoming more their own thing. They have become slightly larger, and certainly stronger, as iterations of the game have moved on, as well as changing from the original brown to greenish to the current grey. The nature of their evil has also changed to some extent, as well as the emphasis that different editions have chosen to place on it. On the other hand, the females do seem to have become more emancipated over time, not that that's anything to do with the race as a whole becoming any "softer".
But now, a quick look at how orcs have been dealt with in a partial selection of D&D and D&D-inspired settings:
It's clear here that the females are, indeed equal to the males, and there isn't really any sign that the society is patriarchal, as the Monster Manual suggests. Surprisingly, given the versions in earlier editions, it turns out that FR orcs have a cultural taboo against non-consensual sex with other races. From a game-play point of view, this is a sensible thing to add, since it removes something that most players are going to find uncomfortable, and it's probably part of the broader aim in 5E of making the game more female-friendly. But it does make one wonder why a chaotic evil race would have a cultural taboo against... well, anything really.
Midnight (3E) portrays a world in which the local analogue of Sauron has won, and thus, while humans are still very common, orcs are arguably the dominant race in the world. In a twist on Tolkien, the local orcs are descended from the magical degradation of dwarves, rather than elves. They have dark grey to black skin, but otherwise have a physique that fits the 3E standard look, and are inherently resistant to cold weather and magical attacks. As shock troops of the dark lord, they seem to be quite organised and capable of forming garrisons and the like, rather than just roving bands of marauders. Unusually, they can cross-breed with dwarves, but not humans. They're actually matriarchal, led by a cadre of magic-wielding priestesses.
The orcs of Mystara physically resemble the 2E sort, and are organised into large and brutal legions with strict military discipline. They regularly associate with the other tribal humanoid races, and some of them have built a civilisation of sorts in a previously abandoned subterranean city. They don't seem to be able to cross-breed with humans, or, indeed, anything else that isn't an orc.
The orcs of Eberron are perhaps the most radical interpretation, a dying race of green-skinned barbarians following a naturalistic religion and mostly just wanting to be left alone. Mention also has to go to the orcs of Warhammer, asexual hairless green-skinned humanoids that are actually composed of a sentient fungus that continually buds off more individuals.
The orcs of HarnWorld come in five different types (also a feature of some other settings, such as Kalamar) but are generally hairy, almost ape-like creatures that are generally smaller than humans. Living in isolated mountain ranges, they are prone to bursting out of their refuges when they run short on resources, descending on the local humans in a ravaging swarm. Females are extremely rare, laying large numbers of eggs at a time, which incubate in dung piles. Given their alien natures, half-orcs, unsurprisingly, don't exist.
Converting the D&D concept of the orc to other game systems should be straightforward enough. They have high strength, low intelligence, and are otherwise broadly human-like, save for a particularly poor temper (often a Disadvantage/Hindrance/etc. in other systems). Apart from combat, and probably survival, the only skill they seem to be particularly adept at is Intimidation. Perhaps the only thing that might be difficult to model directly is their aversion to sunlight, which should provide some actual penalty, but even then, an arbitrary statement of "-10% to combat skills in bright light" (or equivalent value) should suffice.