An archdemon (pl. archdemons) is a high-ranking demon, one of the generals of Hell. Like all demons, they were once human, and either sold their soul or performed enough evil in life to be sentenced to Hell. Those souls whose chief sin in life was pride will eventually be warped into archdemons.
Physiology
Archdemons have no physical form, even in Hell - this is in punishment for their vainglory in life. Instead, when they are not possessing a vessel, they are an indistinct, oily cloud of black smoke. When they are possessing someone, their eyes are a solid inky black, with no variation between pupil, iris, and sclera. Archdemons can take a fully human form temporarily which resembles their form in life, but they cannot maintain it for long before they burn through it (literally, the skin begins to deteriorate). Like all demons, they can render themselves invisible. Also, they are physically capable of overpowering any human, at least when they have a physical form (either their own or a possessed vessel).
To put it simply, iron burns. Any sort of anti-hellspawn weapon will likely be made of iron (and blessed for good measure). Iron will even burn a demon who is possessing a human - but touching iron to the human while they are possessed burns them too. These burns heal eventually, though - as they are specific to the demonic presence, they can heal even when the rest of the body can't.
Holy water burns a demon like acid, though they heal these burns quickly, and it usually just pisses them off. Most demons won't cross through running holy water if they can help it though. As with iron, holy water also burns a possessed vessel, but the vessel will heal quickly - and holy water burns vanish if the demon is exorcised. Demon hunters often spike their drinks with this, as an easy way to tell if one of their guests is possessed. Humans don't notice it any more than regular water.
Magical Characteristics
Archdemons have mastered the capability of harming other demons - even those possessing humans - directly, often without using iron or other methods. Simply by clenching their fist, they can cause excruciating pain to the underlying demonic spirit. They are also highly skilled telekinetics - when possessing a body, they can fling it around the room if they so choose.
There are many ways to get into Hell - and far fewer ways to get OUT. While demons have an easier time of this than your average tortured soul, they still aren't technically supposed to be breaking free, which makes things… difficult. However, if they leave in a spiritual form rather than a corporeal one, it's easier to slip through the cracks - but this means that they don't necessarily have access to a body, which can be annoying. This spiritual form is, essentially, the demon's soul - or what used to be a soul anyway - and appears as a cloud of oily black smoke. Luckily (for them), all demons are capable of possessing human bodies… whether they're already occupied or not. Corpses don't have an opposing soul to deal with, but most demons prefer possessing living bodies (because living bodies aren't decomposed) - they effectively move into the body with its native soul, and overpower that soul, rendering the body's owner incapable of speaking, moving, or in any way controlling the body. While in this state, the demon can rifle through the body's thoughts and memories with some ease, making it very easy for them to impersonate the person whose body they're in, and therefore pass undetected. However, the native soul can resist this invasion. Once out of Hell, all demons can teleport from place to place (usually using crossroads) even between worlds - they cannot, however, use this method to get out of Hell, only to get to and from the corporeal side of the gates.
Possession can be prevented by certain symbols (usually in tattoo form), and can be reversed via an exorcism. However, exorcisms can be dangerous - demons are often not careful with their 'meat suits'. The human body can be damaged beyond its ability to heal while the demon is inside without affecting the demon - they still waltz around in their puppet just fine (in effect, possession keeps the body in stasis - it can't heal, but it also can't die). Once the demon is forced out (or leaves) however, the body is back to being plain ol' human, and all those injuries hit it at once. Depending on the level of injury, if the shock alone doesn't kill the victim, the wounds often will. Archdemons are the hardest demons to exorcise, because they are the most powerful.
There are large sigils called Devil's Traps, generally involving a pentagram inscribed within a circle along with other symbols. Drawn, painted, carved, or inlaid on the ground or ceiling, they are effective traps for most hellspawn. Once they cross into the circle, they can't leave it again - unless the sigil is damaged and a line is broken. Demons who notice the sigil before walking into one usually break it themselves, if they can (if it's inlaid iron, the best they can do is avoid it). Demon hunters typically put these up all over their homes.
An unbroken line of salt placed over a threshold prevents hellspawn from entering - alternately, they cannot cross into a circle made from it. Similarly, hellspawn (particularly hellhounds) cannot abide the plant known as Devil's Shoestring (a common name for members of the genus Viburnum, which comes from their long and flexible roots). The plants are used for protection, placed over windows and doorways to prevent hellspawn from entering. Holy symbols can also be used to repel most hellspawn - however, this is ONLY true if the wielder of the symbol has true faith in it, AND the hellspawn has no legitimate claim. In that case, the hellspawn cannot touch the wielder of the symbol, or directly do them harm (i.e. fling a bookcase at them). Hellspawn are unholy and cannot abide by holiness - however, if the wielder is corrupted, the symbol loses power. A Faustian contract also negates the effect - if you've sold your soul to the Devil, no divine power will protect you.
Society and Habitat
Archdemons are the top of the Hellish hierarchy, the administrators and generals who answer directly to the Devil (and Lilith). When one of them gets out in a possession, the result is typically mass murder. Their Hellish duty is basically to keep lesser demons in line - and of course torment the worst offenders Hell has to the best of their considerable ability.