Do I commit a sinful oath (yamin ghamus) by swearing falsely regarding my residency to obtain housing, even if I don't acquire it?

If you swore an oath about something you know to be untrue, you have committed both lying and swearing an oath upon it. This type of oath is called "Al-Yameen Al-Ghamoos" (the plunging oath), and it is considered one of the major sins. The majority of scholars hold that there is no expiation (kaffarah) for it; rather, sincere repentance to Allah Almighty is obligatory. However, Imam Al-Shafi'i and a group of scholars are of the opinion that expiation is obligatory in addition to repentance. Perhaps combining both is more cautious.