OED:

ˈOddˌfellow, Odd-fellow

[A fanciful appellation: cf. odd a. 9 b.]

A member of a society, fraternity, or ‘order’, organized under this name, with initiatory rites, mystic signs of recognition, and various ‘degrees’ of dignity and honour, for social and benevolent purposes, especially that of rendering assistance to members in sickness, distress, or other need.
   The name ‘Odd Fellows’ appears to have been originally assumed by local clubs formed in various parts of England during the 18th c. for convivial and social purposes, usually with rites of initiation, passwords, and secret ceremonies, supposed to imitate those of Freemasonry. Associations of these clubs were formed from time to time for purposes of mutual recognition; of which that styled the ‘Independent Order of Oddfellows, Manchester Unity’, formed about 1813, has grown into a vast organization, having local branches or ‘lodges’ throughout Great Britain and the Commonwealth, as well as in the United States and some foreign countries. Besides this, there are numerous smaller societies of the same ‘order’ in Great Britain and the Commonwealth; a distinct federation also exists in the United States, which, beginning in 1819 in connexion with the Manchester Union, separated from it in 1842, and is now a great and important organization.

   1795 in R. Humphreys Mem. J. Decastro (1824) 247 As many Grands and Brothers of the Odd Fellows, Bucks, Masonic and other Lodges.    1800 Sporting Mag. XVI. 59/1 A Member of the Odd Fellows.    1811 Lex-Bal., Odd Fellows, a convivial society; the introduction to the most noble grand, arrayed in royal robes, is well worth seeing at the price of becoming a member.    1951 McWhiney & Simkins in A. Dundes Mother Wit (1973) 594/2 This mummery manifests itself in numerous other secret organizations such as the Odd Fellows, the Masons, and the Knights of Columbus.    1854 Thoreau Walden viii. (1886) 170 Men will‥if they can, constrain him to belong to their desperate odd-fellow society.    1887 Pall Mall G. 2 Sept. 8/2 A great gathering of Oddfellows was held last evening at the Masons' Hall tavern‥to welcome the grand master of the Manchester Unity.    1887 Scotsman 16 May 6/5 A General Council Meeting of the Scottish Order of Oddfellows' Friendly Society was held on Saturday at the Oddfellows' Hall, Edinburgh.    1970 New Yorker 14 Nov. 175/1 Members of the Independent Order of Odd Fellows stuck to their symbol of an axe left cleaving into a realistic log.    1977 P. D. James Death of Expert Witness i. 16 A ticket for the local Oddfellows' hop.

Hence ˈOddˌfellowship, the status of an Oddfellow; the principles and organization of the ‘Oddfellows’.

   1871 Daily News 30 June, I am forgetting that some of my readers are, perhaps, unacquainted with the rudiments of Odd-Fellowship.    1883 Chambers's Encycl. VII. 36/1 On its institution in Manchester, the main purpose of Odd⁓fellowship was declared by its laws to be, ‘to render assistance to every brother who may apply through sickness, distress, or otherwise, if he be well attached to the King and government, and faithful to the Order’.    1907 C. E. Jackson Poet Wildey 11 It is the Independent Order of Odd Fellows, or if you like the term better, American Odd Fellowship.    1972 Fairbanks (Alaska) Daily News-Miner 3 Nov. 7/7 Odd Fellowship‥is a benevolent, fraternal order banded together for mutual benefit.

Lingvo:

Oddfellows ['ɔd,feləuz] "Оддфеллоуз", "Чудаки" (общество взаимопомощи [friendly society] с тайным ритуалом масонского типа)