I've experimented extensively with this. Not *exactly* angels per-se, but for otherworldly/preternatural beings of superhuman intelligence. Maybe some of these tricks which (according to CP's and Beta's at least) have worked for me would work for you:
1) As already mentioned, they don't use contractions. One exception is "I've". They use the construct "I've a proposition," or "I've a problem", which sticks out like a sore thumb because "I've got" is the [redundant] usage in common/colloquial speech. TBH I ripped this rule off from an old MS in a medieval setting, but it totally works. My readers instinctively associated the pattern with nobility in the first MS, and it held true for super-beings as well.
2) Depending on who they're interacting with, their pattern varies. When dealing with MORTALS, they used short, declarative, but eloquent speech. I think of it as speaking to a child; you don't bust out your full vocabulary on a four year old, and angels aren't about to get wordy with mortals either. It also limits the interaction, which makes everything your demi-god/whatever says all the more powerful. Generally I don't let them waste words in this situation.
However, when speaking with PEERS, I allow them longer than average dialogue. My dialogue's already pretty realistic- on average a sentence or two max, no wordy-ass paragraph-speeches or monologues in everyday speech- so the readers, again, intrinsically understand what's going on there. They're superbeings, they've been around if not forever than close enough, and they're more patient with each other: less eager to interrupt or argue and more willing to let others speak their piece.
Soapbox Sidenote: It's speak your piece, and hold your peace, damn it. Sorry. Can't tell you how many people've tried to 'correct' that.
3) If they DO argue, they shouldn't be arguing with mortals. EVER. They may try and persuade a mortal, but they're smart enough to know that nobody, in fact, has ever actually won an argument, and therefore it is a waste of their time. Again, imagine children. Parents don't tell their toddler WHY they can't have chocolate before their meals, they just cajole the 2 year old into eating their brussel sprouts with the promise of chocolate because, in fact, two year olds don't have the cognitive capacity to evaluate your logical argument.
You've never heard a toddler say "Gee, dad, that IS a valid, well-constructed argument, I think I'll do that after all."
So, they only argue with each other... but only to a degree. Pretty much every pantheon besides the Judeo-Christian mythos has a bunch of gods with unique, often conflicting views. If the Greek gods weren't bickering all the time, Greek mythology would literally not exist, because that's essentially what's happening in every single damn story.
Still, unless you are going for a pseudo-Greek feel, you want to avoid the teenager affect, most def. They shouldn't be petty. If they're arguing, they should state their facts, possibly offer mutual rebuttals, and- if that fails- accept the fact (again) that virtually nobody in all of history has ever actually won an argument anyways. A sort of agree to disagree type conclusion.
4) I'm going to disagree with one of the other opinions expressed and say non-literal, metaphorical speech would be common. Assuming we're all on the same page about what an angel actually is, I can't POSSIBLY imagine English-as-a-second-language being some sort of barrier for them. I mean, if *I* met an angel and he sounded like the guy who tries to fix my internet from India at 3 AM, I would be seriously disappointed.
As far as I'm concerned, a well-constructed metaphor is a keystone hallmark of a half-decent education. These *are* superbeings after all. My rule is with mortals they're more apt to use similes- because similes are the lower form, and mortals are idiots- and with each other an actual metaphor. Soft-rule, though.
PERFECT example: "The quest stands upon the edge of a knife."
Now, I'll say this: I can't remember if that's a LotR book quote from Tolkien, or something from the film's writers. Either way, it's a perfect example. This is coming from Galadriel, who- barring a few others like Gandalf and Elrond- is pretty much the ultimate personification of longevity, wisdom, and otherworldliness in Lord of the Rings. She could have used any number of lameass similes or even said it bluntly, but NO. She is a badass who's been around LITERALLY ages. Saying it any other way would not have been half as short, sweet, or illustrative.
Compare, for example: "Your chance of failure is great" or "Any misstep could be ruinous" or really any other lame way of saying it that I or anyone can think of off the top of their heads. These examples are just as short, but they don't paint the picture. I mean, YOU LITERALLY PICTURE the gravity of exactly how precarious this whole the-dark-lord-needs-his-ring-back-so-he-can-totally-screw-Middle-Earth-over situation is.
Whoa. I wrote way more than I intended. But if I think of anything else I'll add it haha.