All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First, you should repent to Allaah The Exalted from this blameworthy habit (masturbation) and give up this sin. Your oath by the Quran is an intended binding oath and breaking it necessitates offering expiation.
As you have broken this oath, you are required to expiate for it. The expiation for breaking an oath is to feed ten needy people, or clothe them, or free a slave. If you are able to do any of these three fasting three days as expiation will not clear your liability. However, if you cannot afford to do one of the three aforesaid options (feed ten needy people, or clothe them, or free a slave), you can move to the fasting option. It is more prudent to fast three consecutive days so as to avoid the difference of opinion among Muslim scholars in this regard. If you had enough money to feed ten needy people, then the days you have fasted would not be sufficient to clear your liability and you are required to feed ten needy people as expiation. If you do not have enough money to feed ten needy people, you should fast a third day with the intention of expiating for your broken oath, based on the opinion that the three-day expiatory fast does not have to be observed consecutively. The fact that you committed that sin before completing the fast of the three days does not affect the expiation. However, it is more prudent to start all over again and fast three successive days as expiation for breaking the oath so as to stay away from the difference of opinion among scholars, as clarified above.
It should be noted that reciting the Quran has nothing to do with the expiation for breaking an oath.
Allaah Knows best.