Oia is really beautiful at night. It is great to walk in the village and enjoy the view of the island. The most spectacular is the caldera view with many buidings - most of them hotels with swimming pools thta give a blue colour at night. It looks amazing.:)
Anyway, there are no clubs and places you might go out in Oia. All nightlife is located in the capital of santorini - Fira.
There are many terraces in Oia to enjoy a dinner with woonderful views.
But if you are in a budget, just buy a Gyros Pita, a huge yoghourt and sit on one of the many little walls with wonderful views of the sea, and Thira.
I was lucky enough to see fool moon that night. :-)