At hashkafah.com, the user named "critic" asks:
If someone has body odor (BO) and they can't smell themselves, would they be able to make a bracha?
Also, may they say words of Torah?
[Edit: I figure that if I smelled strongly of BO while spending time with an earthly king, then that king would probably be offended. So I figure the King of Kings might also be offended. Would He?]
Please cite sources.