What is the expiation for an oath such as, "By Allah, you will cause me to have a stroke one day," if the one who swore the oath is unable to fast due to illness and does not possess money? And how does one repent for swearing a false oath or for failing to fulfill an oath?

The father's statement to his children: "By Allah, one day you will cause me to have a stroke" is not considered a binding oath (yamin (definition) mun'aqidah), but rather a vain oath (yamin laghw) for which there is no accountability. If someone swears to do something and does not fulfill their oath, they must offer expiation for the oath. As for the false oath (yamin al-ghamūs) which a person swears intentionally lying, it is one of the major sins, and its due is sincere repentance. If someone swears to something believing it to be true, but it turns out not to be as they swore, and they did not intend to lie, then there is no sin upon them and no expiation.