In section 196 of Philosophical Investigations Wittgenstein writes: “In our failure to understand the use of a word we take it as the expression of a queer process. (As we think of time as a queer medium, of the mind as a queer kind of being.)” Earlier (section 93) he remarks: “One person might say ‘A proposition is the most ordinary thing in the world’ and another ‘A proposition—that’s something very queer!’… Why do we say a proposition is something remarkable? On the one hand, because of the enormous importance attaching to it. (And that is correct). On the other hand this, together with a misunderstanding of the logic of language, seduces us into thinking that something extraordinary, something unique, must be achieved by propositions.—A misunderstanding makes it look to us as if a proposition did something queer.” In Part II of the Investigations (p.215) he tells us of an experience of wrongly imagining a city to be on the right and comments: “’But what is this queer experience?’—Of course it is not queerer than any other; it simply differs in kind from those experiences which we regard as the most fundamental ones, our sense impressions for instance.” And there are other places in which he speaks of a “queer fact” (p.200) and a “queer reaction” (section 288) and says the following (section 428): “’This queer thing, thought’—but it does not strike us as queer when we are thinking. Thought does not strike us as mysterious while we are thinking, but only when we say, as it were retrospectively: ‘How was that possible?’ How was it possible for thought to deal with the very object itself? We feel as if by means of it we had caught reality in our net.” From these scattered remarks we must glean what we can about how Wittgenstein understands the concept of queerness in philosophy. Two ingredients immediately stand out: (i) the queer is unusual and (ii) the queer is not something we should accept at face value. When we speak in this way something has gone wrong in our thought. Wittgenstein thus contrasts the queer with the ordinary; he regards it as unique and remarkable (as we conceive it); he thinks it goes with thinking of something as mysterious; and he takes it to be distinctly dubious and ultimately illusory.  Still, we have more work to do in order to elucidate the concept of the queer fully.
The OED provides a wonderfully succinct definition: “queer: strange; odd”, noting its old sense of “slightly ill” and adding a second meaning of “a homosexual man” described as derogatory. We can see ingredients (i) and (ii) at work in this definition: first, there is the statistical notion in which to be queer is to be infrequent or rare or contrary to the norm; second, there is the pejorative connotation of “strange” and “odd”, as in “oddball” or “strange brew” (though the negativity is not pronounced). Something is queer if it is uncommon and vaguely discreditable (though it can also be seen as remarkable or possibly supernatural). The term “queer” for a homosexual man certainly carries (or did carry) a negative evaluation, no doubt deriving from attitudes towards its designation. The word itself appears in the English language in the sixteenth century and began to be applied to homosexual men only in the nineteenth century, reaching its pejorative height in the twentieth century. Perhaps it was initially used to express rarity (statistical sense) and only later gained a pejorative tone. I suppose Wittgenstein was familiar with this use of the word, though whether its connotations featured in his philosophical use of it I hesitate to say (he was reputed to be an instance of the category himself). Other uses of the term, especially earlier, are not pejorative, but merely descriptive, as in Mr. Rochester’s comment to Jane Eyre: “I sometimes have a queer feeling in regard to you—especially when you are near me, as now: it’s as if I had a string somewhere under my left ribs, tightly and inextricably knotted to a similar string situated in the corresponding quarter of your little frame”. Here the queer feeling is not understood as disagreeable, perhaps the contrary—though rareness is implied (tenderness too). Then we have expressions like” A queer expression came across her face”, where the meaning appears close to “curious”. So the meaning is not irredeemably negative (this will be important in what follows). We must also not forget the old Yorkshire saying, “There’s nowt so queer as folk”, where the meaning is not that homosexuality is universal, but rather that people can be unpredictable and inscrutable (“a rum lot”).
Returning to philosophy, we also have John Mackie’s use of the phrase “the argument from queerness” summed up as follows: “If there were objective moral values, then there would be entities or qualities or relations of a very strange sort, utterly different from anything else in the universe.” Here we observe the use of “strange” as a synonym for “queer”, and also the claim that such objective values would be different from everything else—hence rare, out of the ordinary. I suppose Mackie got the word from Wittgenstein, though he doesn’t cite Wittgenstein in this connection, and his meaning is clearly close to Wittgenstein’s, especially in its pejorative overtones. I think it is fair to report that in this usage the word combines the following elements: unusual, puzzling, queasy-making, mysterious, discreditable, and dubiously applicable to anything real. The queer is what gives us a queer feeling or sensation; it’s how something strikes us not how it is objectively.  Wittgenstein lists time and mind along with meaning in 196—his point being that these two things elicit impressions of queerness from us, though there is nothing objectively queer about time and mind (or meaning). Let’s make a fuller list of the queer and not-queer as these categories are apt to occupy the philosophical intelligence: queer—mind, time, values, meaning, numbers, universals, necessity; not-queer—matter, space, facts, symbols, objects numbered, particulars, actuality. An enormous amount of philosophy has been generated around these contrasts, spurring many a reduction or rejection. The queer is generally frowned upon, maligned, and shown the door. Hence Mackie’s appeal to the concept in arguing against the objective reality of value—“Get away values, you’re queer!”
Now I am not concerned to adjudicate these issues here; my concern is with the concepts involved and how they shape debate (this is meta-philosophy). The word “queer”, like the word “stupid”, is apt to invite the intensifier “fucking”, as in “That’s fucking queer!” It is built for strong disapprobation (consider that intensifier used in conjunction with “queer” for a homosexual man). But such terms often provoke a backlash, an attempt to reclaim them from the lowlands of insult and prejudice. Thus we have the use of “queer” to describe certain kinds of men by those very men—gay men proudly proclaiming themselves queer. We even have “queer studies” and “queer rights” and “queer eye for the straight guy”. And these uses are not etymologically wide of the mark, since “queer” does have a non-pejorative meaning, suggesting uniqueness, interestingness, nonconformity, specialness, exceptionality. Isn’t genius pretty queer? The word became pejorative because of prevailing attitudes, but it is not beyond redemption, so maybe it can be worn as a badge of honor (a bit like “cockney” or “scouser” or ethnic labels generally). Who wants to be commonplace, ordinary, easily understood, and humdrum? Better to be queer! This suggests a comparable move in philosophy: embrace the word “queer” if it describes a view you agree with. Thus one might say in response to Mackie: “Yes, objective values are queer (strange), but that is no objection to them—some things are very different from everything else!” There is no need to tremble in shame as the dreaded label is thrown in your direction—own it, accept it, revel in it. The model here is the use of “mystery” and cognates as labels for certain philosophical positions: maybe the first use of “mysterian” was intended pejoratively, but semantically it is quite apt, so why not embrace it? Just as there is a problem-mystery distinction, so there is a commonplace-queer distinction—and some philosophers might wish to occupy that last niche. If so, they can adopt the label and wear it proudly. Thus we can christen certain philosophers “queerians”, in some instances “new queerians”, while others can be called “anti-queerians” (compare realists and anti-realists). The general doctrine could be labeled “queerianism”, and it can come in different varieties (say, epistemological and metaphysical). Who in particular might be so labeled? Opinions may differ on this but Plato, Frege, and Meinong are good candidates for the label, being generally unconcerned about affronting common sense; I suppose some dualists might accept the label too (“Cartesian queerianism”). There are some things that give us a queer sensation when we contemplate them, but that is perfectly reasonable given their special nature (e.g., abstract unchanging universals, truth-values conceived as objects, non-existent but nevertheless real entities). Moral realists might welcome the label as a way to accentuate their position, better than the bloodless “non-natural” they have been saddled with. Is God queer? Why not—he is certainly not commonplace. Some may even point out, timorously, that matter has got pretty queer in the last three hundred years—queer physics! The word well expresses our feelings when we contemplate certain subject matters, and those feelings are real and appropriate. (Gravity is so queer.) Philosophy has been in flight from the queer given the fearful connotations of that word, but maybe it is time to resist this kind of name-calling by adopting it proudly (assuming it describes your actual position). At least the issues should be debated in these terms and not prejudiced by blatantly derogatory language. What other labels do we have, after all, except those formed by negation from the opposite term (“non-natural”, “nonsensical”, “unintelligible”)? Wittgenstein was onto a genuine and useful philosophical category, despite his disapproval of it; so we should keep it, suitably refurbished. It colorfully adds to our theoretical vocabulary. I would even say it forms a vital part of philosophical consciousness—how our minds work when they are engaged with philosophical problems. It captures the phenomenology.
Once the concept of the queer has been properly absorbed we can ask questions employing it. Is all queerness epistemic or is some found in reality (metaphysical queerness)? Is the queer ever reducible to the non-queer? How are queerness and mystery related? What exactly is the phenomenology of feelings of queerness? Are there different types of queerness (e.g., fact queerness, value queerness)? Are some queer things queerer than other queer things? What is the queerist thing of all? Might everything turn out to be queer? Is non-queerness ultimately an illusion? 
 Thomas Nagel informs me that Wittgenstein used the German world “seltsam” (“strange”) which Anscombe translates as “queer”. This word is never used in German to refer to a male homosexual, so presumably he did not intend any such association. Nagel suggests that Anscombe chose “queer” to emphasize the disturbing element.
 It would be queer indeed if everything we think we know about turned out to be queer. Empiricists took sense impressions to be clearly not queer, but now we recognize that they have a queerness of their own (they stand in a queer relation to the brain). Classical materialists of the mechanistic variety took matter be devoid of queerness, but physics has proved otherwise. Everything can come to seem queer if you think hard enough about it. What is a particular? Isn’t instantiation itself a queer relation (recall Plato’s view of it)? What about causal necessity? How queer is truth? Maybe that old Yorkshire saying needs to be generalized.