delightful demons and angels of awful purpose

Outsiders in D&D are connected to alignment system, but the alignment system has always been ambiguous about whether it refers to psychology or behavior. This opens the room for outsiders whose psychology conforms to the core concept, but with behavior that isn't necessarily expected.

Evil angels are the easiest one, because you've seen them all before. Angels do whatever God asks of them, because God is good. God is indeed the fullness of being, and most of reality is contained within the godhead; all creatures are just a sort of ephemeral leftover. But it must be emphasized that even the angel who commits terrible atrocities, pouring out their philters of doom over Sodom or Jericho, weeps genuinely as they do so. How tragic, that the greatest good should require such! Like an abusive parent, they say "this hurts me more than you," and they are right. They are genuinely eager to avoid as much wrong as can be managed, and will be thankful to anyone who can point out creative solutions to the dilemmas ahead of them.

1d4 Angels of Awful Purpose

1. He announces himself to prophets, holy men, and other worthies, and reveals the Divine Plan; these plans are lies, the prophecies false, that the face of the God might remain hidden, and faith remain faith. He smuggles in worthy moral teachings and the like when possible.
2. She is tasked with ending intelligent life on this plane and has been spending the last few centuries disseminating information on birth control, celibacy, and the like. Her archangelic superior is coming, bearing a heavy heart and the news that the timetable must be moved forward.
3. They tempt men and women with lust, money, and power, that their souls might be tempered, and that the halls of heaven may remain unpolluted. They may every attempt possible to choose those who will be tempted enough for it to be a difficult decision that forces them to bend, but not be broken. But sometimes they miscallibrate.
   
4. It seethes with hatred for all life, for all justice, and for all goodness. It does this because there is another angel - its dear friend, in fact - who has been assigned the awful task of torturing the most wicked soul available, and it therefore needs a way to be wicked (and thus spare others) without hurting anyone.  It plays a dangerous game of doublethink, for its wicked thoughts must be intense without being genuine enough to inspire it to truly act on them. Looking at the increasing evil of men, it binds itself in chains that it might go deeper into depravity and yet not become harmful, but no chain lasts as long as intended.
   

Devils are conniving bootlickers, looking for the best bargain for themselves and holding to it assiduously; they are nothing if not consummate game theorists. Good devils have read Kant and know that, if you're like most beings (and most beings are), choosing to cooperate means that most beings are willing to cooperate. Like angels, "good" devils are smug about their goodness, but they're smug about it because they think they've found a particularly effective trick in the nature of decision theory, and are pleased to have exploited this loophole in the nature of reality. It must be emphasized that even "good" devils don't give a rat's ass about anything that happens to anyone else; indeed, they generally find others' suffering as funny as the normal kind of devil. It's just that they'll alleviate it, given the chance, and grumble about it too.

Chaotic devils have recognized the antagonistic rather than cooperative nature of reality, and that mixed and random strategies are often the right way to deal with an opponent, especially the omnipresent opponent of "everyone who isn't me." "Chaotic" devils employ these mixed strategies every bit as methodically as any other kind of devil; they forgo pleasurable opportunities, think about the long term, keep records of their behavior to spot and correct the existence of observable patterns.

1d4 disconcerting devils

1. He is the Prince of Darkness, the classical Satan. When he first came into being he resolved he would cooperate with God if God cooperated with him, and (to maximize the chance of being cooperated with) to retaliate at any cost to himself if God did not cooperate. God then commanded him to do something other than what he really wanted, so he's at war with an omnipotent being. God works in mysterious ways, doesn't he? Anything you do can and will be turned against you. He tries to sow as much chaos as possible to interfere with the divine's plans; currently, he considers that doing good (or what would immediately seem to a mortal like good) mostly results in this moreso than evil.
   
2. She rides with an order of paladins, righting wrongs and working justice. To let off steam she tortures animals and defiles corpses, since animals and corpses can't rationally commit to any decision theory so you don't need to include them in your Kantian calculations.
   
3. It had a great gig torturing sinners in the depths below - eternal torture of sinners is good altruistic game theory after all, it's committment to a tit-for-tat equilibrium of the grim trigger type. And its fun! Now it's on earth for some reason and doing the rational thing isn't fun anymore. It can deal with this but doesn't like it.
   
4. They cut a deal with a good god, and a deal's a deal.
   

Demons always do whatever they feel like, without any regard for their own or anyone else's interests. "Good" demons feel like helping people, and "lawful" ones feel like obeying particular rules or particular persons, but these are fundamentally whimsies and compulsions, not values or commitments. Some people believe that faeries are actually misclassified demons.

1d4 delightful demons

1. He is a kindly doctor who follows the army, healing all regardless of who they fought for. He loves healing and, if he were ever placed in a long-term situation in which there were no wounded or dying around, he would make some for himself. However, under current conditions, he doesn't need to waste time on that - there are already plenty! If the war ends he might start following another band of violent miscreants, like the PCs.
   
2. She sings at the local tavern for free. She's not especially talented on a technical level, but she enjoys it so much, it's infectious. Every so often she sings something truly beautiful, and when this happens, halfway around the world an innocent drops dead of a heart attack. She is not aware of this, and if made aware of it would not find it interesting.
   
3. It loves to see children laugh and play! It is kidnapping them to its personal Hell where it stuffs them with candy, never have the iPad taken away, and never grow old!
   
4. They whip themselves in the street: "repent! repent!" Everyone snickers that they don't really care about any of that religious stuff and just get off on the whole bit, and everyone is right.

1d4 other oddities

1. Being of axiomatic law and logic that just discovered a flaw in the nature of logic itself, and feels obliged to eliminate it as it sought to eliminate other irregularities.
2. Being of pure balance, gone excessively meta.
3. Negative energy elemental who just found out that life furthers entropy.
4. Positive energy elemental who just found out that life furthers entropy.