The idea of angels probably irritates me more than the idea of gods does. They're practically identical for all we know about them - they're supernatural and a Lot Better Than Mere Mortals, For Sure, but angels serve even higher beings and gods generally don't... but angels take the lead due to the outstanding problem that the book I've sworn to pledge as the truth, the important truth, and nothing but the truth, claims they exist and gives them fairly prominent roles in the story, and yet still manages to skimp on the details of what, exactly, they are, and how, exactly, they matter.
The details it does provide, however, are fairly clearly in direct contradiction to the average person's conception of them. If you manage to get a clear answer out of this hypothetical person on "such a religious question", she is likely to give you three images of what angels look like:
(a) A divinely cute infant or young child, but with wings.
(b) A divinely good-looking woman, but with wings.
(c) A divinely powerful knight, but with wings.
I suppose there's also (d) some combination of the above, usually (b) and (c) because both possible combinations ("female" plus "powerful", and "knight" plus "good-looking") are apparently synergistically attractive, and warrior children don't really seem like a very divine idea.
You may notice a couple of recurring elements, and oddly they're the only ones that come close to approximating biblical descriptions (which tends to multiply both the "divine" and "winged" aspects to redundancy and beyond). I can think of three good reasons the others are wrong:
First, a fact that I've heard circulated frequently and so I presume is fairly well-known, there are very few angels in the Bible who open their messages with a preamble of "Hey there!" It's generally closer to "Fear not". This would seem to rule out (a), for whom this would be unnecessary unless every biblical hero and heroine happened to have a horrible phobia of children with wings*, and (b), whom studies show should worry more about other emotions than fear getting in the way of the message. Similarly, I can't think of any explicitly described manifestations with more than a passing resemblance to a human being, barring when Raphael goes incognito for most of the Book of Tobit, which would seem to eliminate (c) and (d) as well.
* This isn't necessarily a bad assumption to make, but you do have to consider that among such heroines is Mary, who had very explicitly never had children before.
Second, whatever else angels may be, the Bible is fairly specific that humans alone are made in the image of God. If you believe this refers to physical structure, this should suffice; if a reference to God's triunity as mind, body, spirit - well, angels are obviously spiritual beings and occasionally rebellious, which would leave the body as the key difference.
Finally, outside of their allegiances demons and angels are fundamentally identical. There's no support for the notion that good is pretty and evil disgusting (or vice versa) other than peoples' astonishing tendency to merge goodness, truth, and beauty into a single axis; quite the contrary, metaphors involving demonic activity while "disguised as an angel of light" are common. If demons can be light and still evil, angels can be dark and still good.
This is all just a roundabout excuse for me to cite C. S. Lewis, who deals with this quite a lot in The Space Trilogy (another of the world's best stories nobody has ever read), especially because several of his "angels" are the personifications of planets rather than divine messengers. When two manifest near the end of Perelandra it takes them some time to figure out an appearance that won't cause the human protagonist to be physically ill; before they finally settle on sort of metallic colossi, some of their attempts are closer to vertiginous spaces swirling with geometric shapes than any real object. Lewis justified this elsewhere simply by pointing out that everyone expects the forces of evil to be terrible and threatening, and that's all very well, because you can always have faith that the forces of good will swoop in and save you. But when the same applies to the ones in which you trust for salvation... one way or another, you will have to undergo a very radical change of mind.
And when I am explicitly imperfect by nature, and wisdom begins with the perfect fear of an omnipotent God and ends with it being dispelled by his perfect love, that sounds far more real to me than any pretty fledged human.