Is swearing on the Quran to quit cigarettes for life [a permanent oath], or is it temporary, making it permissible to smoke them after Eid?

You must obey your father in quitting smoking because it is forbidden, and your oath on the Mushaf is a binding oath. If by your oath you intended to quit smoking only during the Eid period, then you do not break your oath by smoking afterward, but you incur sin because it is a disobedience and an act of disrespect towards your father. However, if you did not have a specific intention and you smoked, you have broken your oath, in addition to the sin, due to the generality of your wording.