From the second edition (1989):
queer, a.1
(kwɪər) Forms: 6 queir, queyr, que(e)re, 7 quer, 7– queer. [Of doubtful origin.
Commonly regarded as a. G. quer (MHG. twer, see thwart), cross, oblique, squint, perverse, wrongheaded; but the date at which the word appears in Sc. is against this, and the prominent sense does not precisely correspond to any of the uses of G. quer. There are few examples prior to 1700.]

1. a. Strange, odd, peculiar, eccentric, in appearance or character. Also, of questionable character, suspicious, dubious. queer fellow, an eccentric person; also used, esp. in Ireland and in nautical contexts, with varying contextual connotations (see quots.) Cf. quare a.
Possibly some examples illustrate queer a.2

1508 Dunbar Flyting 218 Heir cumis our awin queir Clerk. 1513 Douglas Æneis viii. Prol. 43 The cadgear‥Calland the colȝear ane knaif and culroun full queyr. 1550 Bale Eng. Votaries ii. 21 Ye Chronycles‥contayne muche more truthe than their quere legendes. 1598 Marston Pygmal. i. 138 Show thy queere substance, worthlesse, most absurd. 1621 W. Yonge Diary 27 Aug. (Camden) 43 The emperor is in that quer case, that he is not able to bid battle. 1663 Flagellum or O. Cromwell 109 That the world may see what queer hypocrites his attendants were. 1712 Steele Spect. No. 474 ⁋2 Let me be known all at once for a queer Fellow, and avoided. 1742 Richardson Pamela III. 224, I have heard of many queer Pranks among my Bedfordshire Neighbours. 1840 Dickens Barn. Rudge xxxix, It was a queer fancy‥but he was a queer subject altogether. 1870 H. Smart Race for Wife i, In the queer old room with its still queerer attempts at decoration. 1883 J. F. T. Keane On Blue Water 212 Remembering that incident, the ‘queer-fellow's’ disappearance didn't alarm me very much. 1910 D. W. Bone Brassbounder 64 D'ye think th' queer-fella' is goin' t' pay them prices for 'is kit? 1922 [see middle leg s.v. middle a. 6]. 1932 J. W. Harris Days of Endeavour 17 No matter what ship you serves your time in, you'll find there'll be a queer-feller. 1936 J. Curtis Gilt Kid vi. 60 He'd a good mind to tear over and spoil her lark with the queer fellow. 1939 J. Brophy Queer Fellow 10 When I am ‘making up’ a story,‥I am never my normal self, the man that other people know. Nor dare my normal self return for a moment in the hope of catching the other one, The Queer Fellow, as they say in Ireland, at work. 1958 M. Procter Man in Ambush xii. 134 Mobsters, queer fellows, bar flies and layabouts. 1961 Partridge Dict. Slang Suppl. 1240/2 The queer fella, the person that happens to be in command: Regular Army: late c. 19–20. 1962 Granville Dict. Sailors' Slang 93/2 Queer fella, any merchant seaman who does not conform to the average type. A nautical eccentric. 1966 ‘L. Lane’ ABZ of Scouse ii. 87 Whur's ther queer feller? Where is the boss or foreman whose name I don't know?
absol. 1826 Scott Woodst. (1894) II. 19 His appearance bordered‥upon what is vulgarly called the queer.

b. Of a person (usu. a man): homosexual. Also in phr. as queer as a coot (cf. coot n.1 2b). Hence, of things: pertaining to homosexuals or homosexuality. orig. U.S.

1922 Pract. Value of Scientific Study of Juvenile Delinquents (Children's Bureau, U.S. Dept. of Labor) 8 A young man, easily ascertainable to be unusually fine in other characteristics, is probably ‘queer’ in sex tendency. 1931 G. Irwin Amer. Tramp & Underworld Slang 153 Queer, crooked; criminal. Also applied to effeminate or degenerate men or boys. 1936 J. G. Cozzens Men & Brethren i. 24 ‘He's not queer, or something, is he?’ ‘Lord, no! Worse than that. He's a convert.’ 1937 Listener 10 Mar. (Suppl.) p. vii/2 ‘Queer’, in a specifically sexual sense—a word imported from America. 1939 C. Isherwood Goodbye to Berlin 296 Men dressed as women?‥ Do you mean they're queer? 1952 [see camp a. (and n.5)]. 1958 P. Mortimer Daddy's gone a-Hunting xxx. 169, I suppose they're queer as coots. 1960 [see bent ppl. a. 5c]. 1963 [see gay a. 2c]. 1974 Amer. Speech 1971 XLVI. 81 Female homosexual, lesbian, screwball, queer, lady-lover, minty. 1975 Times 9 July 14/2 Bombus fragrans‥sprinkles himself‥with attar of roses, and‥is as queer as a coot. 1976 A. White Long Silence i. 10 ‘I say, Peter, you're not turning queer by any chance, are you?’ The thought that I might be queer had haunted me.

c. In U.S. colloq. phr. to be queer for (someone or something): to be fond of or ‘keen on’; to be in love with.

1953 W. Burroughs Junkie ii. 28 She began talking about Jack. ‘I'm queer for Jack,’ she said. ‘He works at being a thief just like any job.’ 1956 J. Baldwin Giovanni's Room i. ii. 45 Actually, I'm sort of queer for girls myself. 1957 M. Shulman Rally round Flag, Boys! iv. 51 When‥the cellars were finally snug and dry, Waldo promptly persuaded the homesteaders to fill them with‥a huge, gleaming variety of tools. This took no great persuasion, for‥the average commuter was queer for tools. 1977 Time 28 Mar. 54/2 The sister (Carol Potter) is crazy about him and Francis is queer for her brother (Reed Birney), or so he fears.

2. Not in a normal condition; out of sorts; giddy, faint, or ill: esp. in phr. to feel (or look) queer. Also slang: Drunk.

1781 S. Crisp Let. 1 Mar. in W. H. Hutton Burford Papers (1905) 60, I have been very queer for some time, sleepless and indigestion. 1800 W. B. Rhodes Bomb. Fur. i (1830) 8 We feel ourselves a little queer. 1826 Sporting Mag. XVIII. 285 Galloping‥with a rummish team, and himself queer. 1837 [see earthquaky a.]. 1848 Dickens Dombey i, I am so very queer that I must ask you for a glass of wine and a morsel of that cake. 1885 M. E. Braddon Wyllard's Weird I. i. 39 That business on the railway was enough to make any man feel queer. 1889 J. K. Jerome Three Men in Boat i. 14 So I set my face against the sea trip. Not, as I explained, upon my own account. I was never queer. But I was afraid for George. 1922, 1938 [see come v. 70f]. 1952 A. Christie Mrs McGinty's Dead iv. 28 Either the husband's taken queer, or the old mother.‥ With old McGinty, at least it was only she herself who came over queer. 1978 ‘F. Parrish’ Sting of Honeybee iv. 43 Jake's off queer, wi' a rumblin' stummick.

3. Queer Street: An imaginary street where people in difficulties are supposed to reside; hence, any difficulty, fix, or trouble, bad circumstances, debt, illness, etc. slang.

1811 Lex. Balatron., Queer Street, wrong, improper, contrary to one's wish. It is queer street, a cant phrase, to signify that it is wrong or different to our wish. 1821 P. Egan Real Life in London I. xi. 186 Limping Billy was also evidently in queer-street. 1829 —— Boxiana 2nd Ser. II. 503 Gas let fly right and left, give Pope a tremendous blow over his left ogle, putting him a little into Queer-street. 1837 Lytton E. Maltrav. iv. vii, You are in the wrong box—planted in Queer Street, as we say in London. 1865 Dickens Mut. Fr. iii. i, Queer Street is full of lodgers just at present. 1886 Stevenson Dr. Jekyll i. (ed. 2) 11 The more it looks like Queer Street, the less I ask. 1952 A. Wilson Hemlock & After iii. i. 208 He enjoys a little flutter‥and if he finds himself in Queer Street now and again, I'm sure no one would grudge him his bit of fun. 1963 Times 8 May 9/2 He felt that the levy should not be applied so rigidly as to force companies into Queer Street if their costs rose faster than their incomes. 1980 J. Wainwright Man of Law xlvii. 222 If Patsold talks, Webb's in queer street.

4. Comb., as queer-looking, queer-shaped, queer-tempered.

1825 J. Neal Bro. Jonathan II. 171 A little, modest, queer-looking brown girl. 1838 Dickens Nich. Nick. x, You are the longest-headed, queerest-tempered, old coiner of gold and silver there ever was. 1876 H. Sidgwick in A. & E. M. Sidgwick Henry Sidgwick (1906) v. 323 Stone hovels that a generation ago were the ordinary houses here: things with a hole in the roof, low, queer-shaped. 1891 T. Hardy Tess (1900) 105/1 The queer-shaped flints.