odour n.

c. 1300, "sweet smell, scent, fragrance," from Anglo-French odour, from Old French odor "smell, perfume, fragrance" (12c., Modern French odeur) and directly from Latin odor "a smell, a scent" (pleasant or disagreeable), from PIE root *hed- "to smell" (source also of Latin olere "emit a smell, to smell of," with Sabine -l- for -d-; Greek ozein "to smell," odmē "odor, scent;" Armenian hotim "I smell;" Lithuanian uodžiu, uosti "to smell, sniff;" Old Czech jadati "to investigate, explore").

Neutral sense of "smell as an inherent property of matter; scent or fragrance whether pleasant or not" is from late 14c. "[W]hen used without a qualifying adjunct, the word usually denotes an agreeable smell" [Century Dictionary, 1895]. Good or bad odor, in reference to repute or esteem, is from 1835. Odor of sanctity (1756) is from French odeur de sainteté (17c.) "sweet or balsamic scent said to be exhaled by the bodies of eminent saints at death or upon disinterment." In Middle English odor also had a figurative sense of "spiritual fragrance of Christ's sacrifice." 

word-forming element making nouns of quality, state, or condition, from Middle English -our, from Old French -our (Modern French -eur), from Latin -orem (nominative -or), a suffix added to past participle verbal stems. Also in some cases from Latin -atorem (nominative -ator).

In U.S., via Noah Webster, -or is nearly universal (but not in glamour), while in Britain -our is used in most cases (but with many exceptions: author, error, tenor, senator, ancestor, horror etc.). The -our form predominated after c. 1300, but Mencken reports that the first three folios of Shakespeare's plays used both spellings indiscriminately and with equal frequency; only in the Fourth Folio of 1685 does -our become consistent.

A partial revival of -or on the Latin model took place from 16c. (governour began to lose its -u- 16c. and it was gone by 19c.), and also among phonetic spellers in both England and America (John Wesley wrote that -or was "a fashionable impropriety" in England in 1791).

Webster criticized the habit of deleting -u- in -our words in his first speller ("A Grammatical Institute of the English Language," commonly called the Blue-Black Speller) in 1783. His own deletion of the -u- began with the revision of 1804, and was enshrined in the influential "Comprehensive Dictionary of the English Language" (1806), which also established in the U.S. -ic for British -ick and -er for -re, along with many other attempts at reformed spelling which never caught on (such as masheen for machine). His attempt to justify them on the grounds of etymology and the custom of great writers does not hold up.

Fowler notes the British drop the -u- when forming adjectives ending in -orous (humorous) and derivatives in -ation and -ize, in which cases the Latin origin is respected (such as vaporize). When the Americans began to consistently spell it one way, however, the British reflexively hardened their insistence on the other. "The American abolition of -our in such words as honour and favour has probably retarded rather than quickened English progress in the same direction." [Fowler]