What is the religiously lawful way out for the wife who swore an oath that she would not undergo the medical tests necessary for pregnancy, and invoked a curse upon herself if her husband did not get a brain scan, while he does not possess the money for it and Allah has relieved him of pain?

If the reason for the wife's oath was her eagerness to diagnose and treat an illness, and Allah facilitated the cure, then she is not obliged to offer expiation for undergoing medical tests. A Muslim should guard his oaths and not rush into swearing them. Allah Almighty says: "And guard your oaths. Thus does Allah make clear to you His verses that you may be grateful." It is not permissible for a Muslim to invoke evil upon himself.