Even thinking about this question makes me gag; that is how bad the situation is with a co-worker who has a terrible body odor problem. He doesn’t seem to be aware of it, but everyone else is. None of us feels comfortable saying anything because we don’t want to embarrass him, but it’s awful. What do we do?
If no one in the office wants to privately tell him that he has a problem, then your manager or department head has to step up and speak to him. It may be that he has a medical or dietary situation that is causing him to emanate a strong odor, which she can say, suggesting that he speak to his doctor. She can add that if she had such a problem she would want someone to tell her, so she hopes he takes her suggestions as positive comments and finds a way to resolve this problem. One or more of you has to ask her to deal with this in case she is unaware of the situation.