Does a divorce occur if the husband says: "I am divorced if the roof of the house is above my head and the head of a strange man without a mahram present," and then a non-mahram man enters the house for one second merely to take something, knowing that the wife exited immediately, and that the husband's intention was to threaten, not to divorce?

If the husband explicitly states that his conditioning of divorce on his wife being with a non-mahram man was intended to mean seclusion (khalwa), and no seclusion occurred, then no divorce takes place, because an oath is based on the intention of the swearer. As for the intention of threatening, it is not given any weight by the majority of scholars. Sheikh Al-Islam Ibn Taymiyyah holds that an expiation for an oath (kaffarat yamin) is required if the husband did not intend divorce.