Mathraki doesn't host any large festival. The small size of the island, the few inhabitants and the lack of facilities work reluctantly for the organizing of feasts or festivals that you can see in most of the Greek islands. In special occasions, though, there might be a religious festival but this happens quietly rarely.
If you want to attend a festival, better go to the neighboring island of Corfu, where religious festivals and panigyria are frequently held in summer, on the name day of some saints. In these festivals, a Mass is held in the church of the saint and then traditional music and dancing follow in the village square.
Another popular festival in Corfu is held on August 11th. Varkarola is organized to honor the protector of the island, Saint Spyridon, who saved the inhabitants from a Turkish attack in the 18th century. Such a festival is also held in Ereikoussa, a small island close to Mathraki.