What is the ruling on someone who swore mighty oaths not to speak to a person, then invoked upon herself barrenness if she were to speak to him, and then was compelled to speak to him?

If you swore an oath not to speak to someone, and then you spoke to them, whether out of necessity or not, you owe a single expiation for breaking an oath. However, if your intention with the oath was not to speak to them by choice, then in that case, you do not break your oath by speaking to them out of necessity, for intention is considered in oaths. The Prophet forbade supplicating against oneself except with good.