I think you're referencing some of the more horror genre level depictions of angels and demons Tankerace, where it's intended that the humans basically be helpless before their opponent(s) and only some Deux Ex Machina saves the day (if the day gets saved at all). Those like that or the Cthulu style settings might have such power levels but more are considerably less. Look at The Exorcist for example, the demon or demons possessing the girl had very little power and mostly resorted to fear and intimidation tactics. For stories of demonic (and angelic) possession the host rarely ends up much more powerful than it started save in settings where it's approaching the horror genre (like Buffy or Angel). Unbeatable juggernauts with nigh-infinite power won't make for a great game for anyone but a killer GM perhaps, have to give the players at least a chance.
In a Super-hero game context angels and demons would range in power roughly between that of say Spider-man to Thor, with only the serious elder types being at the Thor end of the spectrum, anything higher wouldn't have reason or motivation to manifest on the Earth plane (and might not even be able to). If you subscribe to the idea that killing it really just sends it back to its originating plane then it'd have a period where it couldn't return as it recovered from the defeat. Many such stories consider the defeat as a loss of prestige and complex rules governsuch manifesting in the first place and it'd be very risky for a demon or angel to try and circumvent things and just pop up a turn after being 'killed'. This doesn't stop them from calling in favors and having others take over instead of course while they're constrained.
Angels are often linked with the elements, particular air so one could see some measure of air animation or weather control (depending on how you fit to the genre while using them in a super-hero game you could even include some uncontrollable Weather Control that results in storms and lightning events as a result of sufficient power being manifested by the angel or demon heralding their influence in the material world). Demons on the flip side are generally linked to fire, particularly magical soul-searing fire called Hellfire. Damage from Hellfire can eventually erode someone's Psyche until their mind shatters, possibly permanently.
Angels and Demons both often have at least a minimum level of ability of Human Changeling to appear like a human (and often being genderless creatures of the spirit the gender that they select is totally at their discretion and whim) and blend in although not all do or choose to use it if they do have it. Angels generally fly as they're seen to have wings (sometimes multiple pairs of wings to indicate angelic rank) and demons that haven't been forcibly defeated or banished often have a form of dimensional teleport by teleporting back to their hell and then returning to earth wherever they desire.
Demons in particular are often considered strong, tough, and resistant to damage due to how they're depicted, and in possession of wicked claws and if bestial enough fangs. For the more fanciful versions of Christian design they also have a pitchfork for tormenting targets on a physical and spiritual level.
Angels are often surprisingly strong for their apparent slenderness, sometimes considered to wield a sword for smiting evil, and automatically defeat any demons they oppose directly. Of course for a story where it's a crazed angel looking to destroy and the group has a heroic demon attempting to earn forgiveness and get into Heaven once again he may prove sufficiently pure of heart to not be subject to the automatic defeat clause if it's included. Otherwise it could be his fighting on even when hope doesn't exist somehow wakes the angel up to its madness and it surrenders and gives up its mad crusade (and earns the demon hero some bonus karma for fighting on even when fated to lose). There's also the divine light (for an angel that's not crazed) that will burn evil creatures and undead (although humans it'd more cause feelings of euphoria for the good ones at that feeling of God's Presense and discomfort to physical pain for evil humans depending on how evil they are and how close to possible redemption).
The option of possession is possible if you're covering the range of powers sporatically shown by both sides, which could be handled in a number of ways (since the host body doesn't have to gain any extra powers). The Serial Immortality power can be seen as a good list of possible ways to reflect the possession. An angel might reanimate a corpse and set up 'house' in it rather than impose on someone's God-given Free Will and spruce it up with some powers suitable to an angel (including wings that can be manifested at will) while a Demon might go with that (easier to use a dead body without a soul to get in the way) or it might possess someone and reshape their body while they're inside screaming futilely for release (and if the heroes kill the body they're left with the dead victim and no karma while the demon returns home to recover before doing it all over again).
The end result is how much do you want the angels or demons you use (or half-breeds) to have and let get away with in a game, how close to the upper end do you feel appropriate.
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[
www.classicmarvelforever.com] - Nightmask Character Sheet
[
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[
www.schlockmercenary.com] - The Gospel of Uncle Ben
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