In American English, odor is the preferred spelling of the noun referring to a property detected by the sense of smell. In all other main varieties of English, odour is the preferred spelling. This spelling difference extends to odorless and odourless, but it does not extend to odorous and malodorous, which are so spelled in all varieties of English.
Along with this is the unpleasant smell of body odor and lack of dental hygiene. [Washington Post]
In the late 1930s, though, that odor did nothing to deter a young bullfighting-obsessed American writer living in the city from frequenting the slaughterhouse. [New York Times]
Grant’s father was a leather tanner, which meant he was surrounded by animal odors. [Post-Tribune]
Outside the U.S.
The other one is found in central Thailand, but differs in its colour and odour. [BBC]
Perhaps better movie odours might even improve the dispositions of movie reviewers. [Globe and Mail]
As the pressure builds in a chamber, it expands and releases an odour through a tiny hole. [News.com.au]