Medieval scholastic philosophy posited that angels exist as purely intellectual beings. In other words, angels have no corporeal substance. This doesn’t mean that angels are ethereal or vaporous creatures. Rather, angels have no material form at all. This idea has several interesting consequences. Although angels are purely intellectual beings, they can assume material form. When doing so, however, these bodies are not alive. Angels do not experience sensory impressions the way material creatures do. They do not receive knowledge of the world around them from their senses, but instead receive knowledge immediately via the intellect unimpeded by physical limitations.
Thus, while embodied, angels are immune to any thing which requires a sensing, living body to be acted upon. Angels cannot be poisoned, do not require food or water or air, cannot be fooled by Stealth or tricked by illusions, do not feel physical pain or pleasure, et cetera. Angels always win opposed skill checks related to mental ability scores. You can’t Bluff or Intimidate an angel. Angels don’t have to make Perception checks; they always perceive via pure intellectual means unencumbered by the vagaries of physical senses. Since an angel’s temporary body is composed of reshaped matter, it can be damaged. Effects that can harm inanimate objects can harm angels, at least insofar as such effects may destroy the angel’s fake body.
When not embodied, angels are invisibile, completely immaterial, and are not physically limited in the way corporeal creatures are. Time and space, for example, are not barriers to an angel. Angels do not travel. They simply arrive and depart, sort of like an always active, unlimited greater teleport. When engaging in divination, angels are no more likely to err than the powers they serve. Also, they do not have to learn, since learning is a corporeal activity mediated through the senses over time. Angels simply know, immediately and fully.
Since, according to the medieval scholastics, not all angels are good, the same characteristics posited about angels also apply to demons and devils.
In game terms, adopting these medieval theories about angels can be handled largely as background data. The actual stats of the creatures need not be changed. Reactions that ought not occur (such as an intellectual creature failing a Sense Motive check) can be written off as some sort of trick, the result of hubris on the creature’s part, et cetera. Then, when the time is right, you can spring the full power of such a creature on the party, having laid the groundwork with suitable hints related to player character Knowledge checks and so forth. Imagine your players’ surprise and annoyance when they discover that the demon they’ve killed isn’t really destroyed, but instead has been shadowing them while immaterial, waiting for a chance to spring its trap.