What is the ruling on a man using strong perfume at the time of prayer or when going out to work, and does the ruling on a woman using perfume apply to him?

There is no objection to men wearing perfume when leaving their homes; in fact, it is legislatively مطلوب (desirable/recommended) when going out for Jumu'ah prayer, as stated in the Hadith narrated by Muslim: "Ghusl (ritual bath) on the day of Jumu'ah is obligatory for every adult, and he should apply whatever perfume he can afford." Men are not to be equated with women in this regard, for Allah has encouraged men to wear perfume when going out for Jumu'ah, and has forbidden it for women.