If someone swore to a girl, "If you don't do that, then consider what's between us over," and she didn't do it, does he owe expiation if he wants to speak with her again?

This girl is a stranger to you, and your communication with her should be only when necessary and to the extent of that necessity, while observing the Shariah guidelines to avoid temptation. Nothing is incumbent upon you regarding your oath unless, by the phrase "consider that what is between us is over," you intended that you would not speak with her, and you intended by writing this as an oath. In that case, you are bound by the expiation for breaking an oath if you break it, because writing an oath is a metaphorical expression that refers back to the intention of the one who made it. Divorce applies to a wife and does not affect a woman who is a stranger.