Is expiation obligatory for one who swore an oath upon the Quran not to smoke and not to commit forbidden acts, then broke his oath, and does the oath become void after breaking it with the obligation of expiation if he smokes a second time?

If you swore by Allah Almighty while your hand was on the Qur’an, or if you swore by the Qur’an, your oath is binding, even if your intention was not firm. As for your saying "Insha’Allah" (God willing) after the oath, it is an exception that has conditions. If these conditions are met, the oath is dissolved, and no expiation is required of you. If the conditions for the exception are not met, you are required to offer a single expiation for the oath if you break it, unless the wording of the oath implies repetition or you intended to repeatedly break it, in which case the expiation would be repeated. The intention of the person who made you swear is not taken into consideration.