Meganisi is not the place to go for a wild nightlife. It hosts only a few seaside cafeterias, most of which are found in Vathi. There are also many taverns to enjoy a fresh, tasty dish. In any case, things at night are quiet.
If you want a bit of nightlife, you should go to the neighboring island of Lefkada, where you will find plenty of bars and clubs open till the late hours. Meganisi is connected to Lefkada by ferry through the port of Nydri.