In Heaven, there are 9 Major Choirs and one "rogue element" who serve the Archangels.
Seraphim, the Most Humble, beings of Truth and light who work to dissolve the lies of the Horde and bring humanity away from the temptation of deceiving themselves and others.
Cherubim, the Guardians, angels who do what they can to protect and preserve that which is precious to the Symphony and mankind, selfless bodyguards who ask for nothing more than to love that which they guard.
Ofanim, the Wheels, racing with unlimited speed across the skies of Heaven, rushing to wherever someone needs help, never stopping for anyone or anything.
Elohim, the Powers, angels of perfect emotional balance and stability, keeping there own emotions in check so that they may bring balance and integrity to others.
Malakim, the Virtues, beings who hunt down demons to bring them to divine justice, cleansing the Symphony of infernal taint. However... as is the nature of free will... even these paragons of God can turn their backs on Heaven.
Lilim, the Gifters, sensuous angels who weave complex webs of give and (little) take with mankind, promoting selflessness and hard work. They are the beautiful Daughters of Lilith, the Prime Woman, and stand unique among the Host.
Kyriotates, the Dominations, alien creatures who have the unique ability to possess living creatures and use them like corporeal vehicles for their purposes. Eccentric and bubbly, they do what they can to give humanity that little push so that they may succeed.
Mercurians, the Friends, angels who look much like humans with white wings, perceiving the endless web of life that flows in and out of all human souls. They guide humans together, giving them a friend when no one else will be there for them.
Grigori, the Giants, closest to mankind, and indeed, some say they are more human than a human. Some could not reconcile their human desires with their celestial natures and neglected their duties, eventually being cast from Heaven until they had repented, or Fell.
Holy ethereals, spirits from the Marches who have chosen to help mankind and Heaven by serving them as best they can. They have no special ability aside from the unique nature of being made from human dreams, but they still accept powers from various Words.
In Hell, there are 9 Major Bands who serve the Princes. Balseraphim, the Liars, twisted creatures who believe they are always telling the truth, when in fact they are only perverting the Symphony to fit their worldviews. Masters of propaganda, they drive humans to the Pit to serve their Lord and Master, Michael.
Djinn, the Stalkers, apathetic demons who pretend to not care, when in fact their greatest need is to be loved and to love once again. They keep track of anything and everything, but are careful to not let their apathy turn into sudden burning obsession -- or even worse, love.
Calabim, the Destroyers, the motion and speed of the Ofanim turned into entropy and destruction. Shock troops of Hell, they only desire to tear things apart with large explosions and heavy weapons.
Habbalah, the Punishers, creatures of emotion and extremes, who desire only to root out the weak creatures known as humans for being so weak. They serve Hell believing they are angels, and refuse to accept the idea they are actually deluded demons.
Honorium, the Warriors, the honorable soldiers of Hell, a rare yet terrifying sight. They fight for the honor of Hell and Michael, and are the most violent demons in Hell next to the Calabim. Unlike Calabim though, their wrath is cold and controlled, and they are submissive to their dark Princes.
Dark Lilim, the Tempters, Lilim who Fell from Heaven and gave up there freedom for the bleak servitude underneath the tyrannical Princes. They, much like their heavenly sisters, weave complex webs of give and take, but they are always playing to win more than they give. They are the sultry temptresses, the hard-faced deal makers, the ones who give humans what they want for their immortal souls in return. Or maybe just a little favor.
Shedim, the Corruptors, monstrous creatures who's only desire is to pervert and corrupt the minds of humanity to the whims and ideals of Hell, reducing the human to a slavering beast of unredeemable stature.
Impudites, the Takers, lovers of humanity. They integrate themselves with humans and suck them dry of their vital Essence, and then act like living Essence batteries for other demons, fueling the War effort and leaving humans with nothing to defend themselves with.
Dark Grigori, the Skulkers, selfish creatures who wish to hide among humans, always observing from a quiet distance, unseen and unheard. They serve Hell by reducing the disturbance caused by demons, and can breed with humans to create Children of the Dark Grigori, or far more insidious, the hideous Nephallim.
Humans can become a number of things in INverse. They can be Soldiers of God, Soldiers of Hell, Pagan Soldiers, Hellsworn, Undead, Divine Saints and Infernal Saints. Michael leaves no resource untapped, and Infernal Saints are a huge asset to the War, and thus any Prince can now send damned souls up in vessels to do their bidding. Treat Infernal Saints exactly as Divine Saints. There is also a new type of undead, Liches, explained in detail where appropriate. Soldiers are more common in INverse, since Michael and Heaven do not make as much of an effort to keep themselves concealed, although Heaven fights hard to keep celestial interference down to a minimum, so that humans may grow unstunted.
Unlike in canon, Malakim can Fall, although this is rare and difficult to do for them. When a Malakim Falls she becomes an Honorium, a Warrior. They are detailed in their own section. Honorium can be made when a Malakim willingly accepts an Infernal Force, Falls, is created by a Prince, or (very rarely) fledges in Hell from an Imp.
Lilim are born in Heaven, and are detailed in Lilith's write up. When they Fall they become Dark Lilim, and are treated like canon Lilim. One note though -- there are no Free Lilim in Hell, the Fallen Lilim either binds herself to a Prince, or becomes Force feed for other projects. More often though, Marc sweeps them up and forces them into his service.
There are Grigori and Dark Grigori (referred to as Skulkers for ease), and both serve Heaven equally, although there remains a sizeable population of Outcast Grigori, both Fallen and not, who stay among humanity and do as they see fit.
Relievers fledge at 9 Forces into one of the 8 Major Choirs.
There are many "lesser demons" in Hell, but the two important kinds are Gremlin and Imps. Imps can fledge into any of the 8 Major Bands at 9 Forces (not 7 like in canon, Michael choose quality or quantity), and Gremlins can fledge into Calabim, Shedim or Djinn at only 7 Forces. Other lesser demons can fledge into any of the 8 Major Bands at random amounts of Forces, but this is unreliable. Imps are the most stable breed of lesser demon.
Considering that all the canon Superiors are now on opposite sides as it where, how did this affect the history and life of mankind? There is going to be a timeline eventually that details how things went, so this only details how things are different in this world for humans.
First, technology was always treated as an intimate and important tool, and the typical modern day image of technology being hip, cool, and for the elite is absent. It is much "warmer" in this world, and the line between the techno have's and the techno have not's is absent. People have come to expect that many things in life will go wrong or fail altogether, and great success is rarer and much more praised. Although people have the attitude that they will fail, this is coupled with the expectation that they will have hope still, and struggle on until they do succeed. People tend to be a little more selfless and loving, a little more aware of others around them. The most popular heroes in the media and literature where the ones who failed time and time again, but still struggled on. For example, Beowulf never defeated Grendel in his story. The kingdom died, but Beowulf still fought on to defeat the monster, failing over and over again. People are also much faster to believe in the supernatural, and religious fervor is at a level that would shock many from the canon world. Life tends to be a little shorter, lived a little faster, and not often with a happy ending. Life goes bad for most, but not without some truly happy periods of time and being, and maybe even a joyful end. Soldiers, no matter what side they serve (though it matters most to Soldiers of God) have an easier time of getting work done without as many problems with society.
On the side of history, much has gone the same, with a few notable exceptions, especially the the dark reign of "The Black King M'kil", who killed Charlemagne and attempted to take over all of the eastern world, only barely succeeding, having been defeated by a powerful general named Ba'il, and his white robed companion (said to be a sorceress), Lucca, and numerous other mysterious figures.
All in all, one would be pressed at first to see the minute details of difference in this world from the canon one. But stay there long enough, and you too would begin to feel it -- a darkness, a shadow being cast over your own, the feeling of being eclipsed by a terrible force far greater than you can possibly hope to comprehend. Your insides go cold, and you feel like you've been turned inside out, and dumped upside down.