Toss eggplant with 1/4 cup salt and drain in a colander set over a bowl, covered, at room temperature 4 hours. (Eggplant will turn brown.) Discard liquid in bowl.
Gently squeeze handfuls of eggplant. Bring water and vinegar to a boil in a medium pot. Add eggplant and boil, stirring occasionally, until tender, 2 to 3 minutes. Drain in colander, then set colander over a bowl and cover eggplant with a plate and a weight (such as a large heavy can).
Continue to drain, covered and chilled, 8 to 12 hours. Discard liquid in bowl. Gently squeeze handfuls of eggplant to remove excess liquid, then pat dry.
Stir together eggplant, garlic, oregano, 1/2 teaspoon pepper, and 1 cup oil in a bowl. Transfer to a 1-quart jar or other container with a tight-fitting lid and add just enough olive oil to cover eggplant. Marinate eggplant, covered and chilled, at least 4 hours. Bring to room temperature before serving.