Perhaps one of the most difficult things I ever had to do as a manager of staff was to talk to someone about their 'body odour'. Can anyone think of a term to use and appropriate language in which the subject might be introduced in a private conversation?
I am a teacher, and I have had to bring that up before. There are two strategies.
Address a group during a meeting, gently pointing out that being in close quarters, this is a reminder we all have to be especially aware of our personal hygiene habits, such as showering, deodorant. Trust me, he or she will get the message and you haven't specifically mentioned odor. You might assume this will cause sensitivity and feelings of self-consciousness in your non-odorous employees, but quite the contrary. Most likely they too have observed the odorous employee and will recognize and appreciate your efforts.
Discreetly take the odorous employee aside and speak directly to him/her, again, gently pointing out that being in close quarters, we all have to be especially aware of our personal hygiene habits, such as showering, deodorant.
Regardless of strategy, it really helps if you are soft-spoken and respectful and you treat the matter with sensitivity.
Depending on the make-up of the group, such as a room of young men, one can facetiously refer to the "manly funk" permeating the room and mention that though they may each be as physically imposing as King Kong, it does not mean that they need to smell like him.
In a group of mixed ages and genders, it would be collectively embarrassing to mention body odor so maybe it could be addressed by saying that the room seems "stuffy" (as a euphemism) and suggest that a window be opened or someone pop for a bottle of Febreze air freshener to be sprayed before the day begins (with special concentration on the offender's workspace...surreptitiously, of course!)
To discuss the topic delicately, I'd enquire about health, using a dialog on the order of "Mr. X, are you alright? I've noticed a body odor around you that suggests to me that you might want to consult a physician. I'd feel badly if your you had a health condition, and something happened because I didn't say anything."