Is it permissible to pray despite a smell emanating from the male organ?

If the odor is due to the emission of wind from the front private part (qabul), then there is a difference of opinion among the jurists:

Malikis and Hanafis: They hold that it does not nullify ablution (wudu’). They consider wind emitted from the qabul to be like belching or merely a twitch, which does not invalidate ablution. Hanbalis: It nullifies ablution if there is certainty of wind emission, because it issues from one of the two private parts. However, if it is merely a doubt, it does not nullify ablution. Shafi'is: They hold that ablution is void. Everything that issues from the two private parts (the front or rear private part of a man or a woman) nullifies ablution, whether it is urine, wind, or anything else, and there is no distinction between what is rare and what is customary.

However, if the mentioned odor has no relation to wind that nullifies ablution, then it does not result in the nullification of ablution, nor does it prevent or invalidate prayer. It is advisable to be diligent about cleanliness and to use perfumes.