In a sense, a sort of triple oxymoron. But only if one knows what the individual words mean.
Oddly rather agreeable.
That’s one set of meanings, anyway. It doesn’t quite ring of an oxymoron, though.
Is this thread a birthday present for MTGuru? 
Exclusively thoroughly foolish?
Singularly generally precise?
“Triple oxymoron” seems difficult to imagine. Sharp or dull, dull or sharp. Reminds me of those Ginsu knives that were razor sharp so you could cut a tin can.
exceptionally somewhat accurate. (that doesn’t work, does it?)
Oddly soundless city?
Well, of course, “peculiar” doesn’t really mean odd, but rather something like ‘uniquely individual’, “quite” is a rather absolute term and “nice” is just far too precise.
I should have been born in the 19c. 
Now that is poetry. Lovely.
Do keep 'em coming folks!
Do you mean “quite” as in “he was quite friendly but…” or as in “Quite right !”? Those are usages that I find make “she was quite good-looking” rather* ambiguous. Would ambiguity destroy the oxymoron (triple or otherwise) ?
Rather precisely ambiguous.
In Merkin Ænglisc, “peculiar” seems to only retain the sense of “uniquely individual” in formations such as “a custom peculiar to that group”, but for me it still carries the undertone of a judgment of oddness on the part of the speaker; to avoid any scent of that, I would more likely say “specific”. “Quite” means anything from “(a bit more than) rather” to “very (much)” to “especially” to “exactly”; precision of meaning seems not to be all that important in its use as an emphatic device in American speech, and indeed it leaves things up to some interpretation, but we don’t seem to care too much about that although to a degree we do rely on context. For example, contextually my use of “quite” would mean “exactly” in the following: “As for your explanation of ‘nice’ above, I’m not quite sure whether you are describing its character or giving a definition.”
To further confuse the issue, contextually I would mean “very much” in the following: “This is quite an interesting topic.”
Although interpretation can vary (and it could depend on hearing the speaker’s tone), including the meaning of “very”, here we also get closer to the noncommittal “(a bit more than) rather”, thus: “That’s quite interesting.”
If your meaning is “rather”, “quite” is a bit more friendly-sounding in that it suggests that the topic has your interest, which may not in fact be true. In that use, it can also express sarcasm.
With ‘quite’ it’s not only context. The nature of the noun that it is applied to can show the meaning. If it is something that lies on an open-ended scale then I think it usually means ‘very’ - “quite big”, “quite attractive” etc. If there is an end to the scale it is more likely to mean that we are at the absolute end of the scale as in “quite full”. But “quite unique” would be tautology - for the purpose of emphasis maybe.
You mentioned tautology, David (see below). Well, “quite right” is also a tautology, of course. If it’s right, it’s right.
“Quite” isn’t applied to a noun. It’s a qualifying adverb, which is often applied to an adjective, may be applied to another adverb, but never to a noun.
To me, “quite” simply means “absolutely”. So, the phrase “quite full” when applied to a container of some sort, can only mean that the container is full to the point where it cannot hold any more. I think the rot set in when people first started using it in phrases such as “quite delicious”, “quite entertaining” etc, where even if you used the word “absolutely” you couldn’t in fact mean “absolutely” since the concept to which you’re referring is a subjective one. And then, after that, maybe the sarcasm that Nano refers to diluted tthe word’s meaning even further.
I’ll get back to the other words soon (“soon” being a word which, as any fule kno, means “immediately” 
).
Yes, that’s why I switched to “quite full” in the subsequent post. I toyed with ‘quite certain’ but phrases like 'how certain are you ?" make that tricky.
And thanks for the correction about the adjective - I was too rushed to think it through
I don’t think it is that ‘delightful’ and ‘delicious’ are subjective but that, like ‘big’ they are open-ended. They may be open-ended because they are subjective but in the context of ‘quite’ it is what they share with ‘big’ but don’t share with ‘full’ that is relevant.
I’m not quite sure what you mean, David. But I think it’s possible that I might be in agreement with you. I’m struggling to apply example words that will convince me … “full” doesn’t quite do it for me, for some reason. Not nice enough, maybe.
I am suggesting that ‘completely delicious’ and ‘half delicious’ are as meaningless as ‘completely big’ and ‘half big’, but that ‘half full’ and ‘completely full’ make sense. I am not sure about ‘partially certain’ because the question “How certain are you about that ?” is sensible even though an answer of “quite certain” would not be ambiguous to most people.
I wish to here state for the record that despite all the good and compelling points given here so far, in conversational mode I will continue to knowingly engage in useless tautology ( AND split infinitives ) as a rhetorical device for the sake of registering subtleties of emphasis. My English has room for poetry enough to unfold a flower and hatch dragons.
That said, of course tidiness counts whatever your discursive strategy. I’m workin’ on it.
No one is going to want to clean up after yer dragons, ya know 
Some have tried. But as you hint, fouled armor is going to be a sure thing in any case.
I would certainly suggest other apparel.
