What is the ruling on swearing to a guest, saying, "By Allah, lunch is at my place," and his responding with, "No, by Allah, I won't come to you"?

A Muslim should not excessively swear by Allah. If he swears an oath concerning someone else, he must fulfill his oath unless it involves hardship. Regarding swearing oaths concerning the actions of others: if the oath was unintentional, it falls under 'Laghw al-Yamin' (a vain or idle oath), and there is no accountability for it. However, if it was intentional, and the person sworn about refuses to perform the action, then the swearer is the one who has broken the oath and is liable for expiation, unless the person sworn about was compelled, in which case no one has broken the oath. Some scholars have differentiated between a situation where the swearer believes the person sworn about will obey him, in which case there is no expiation, and a situation where he does not believe so, in which case he breaks the oath and expiation is due.