Line a colander with paper towels and set it over a large bowl. Add the yogurt to the colander and let drain, covered and chilled, about 4 hours or as much as 8.
Grate the cucumbers and squeeze between paper towels to remove excess moisture.Add to a bowl along with the yogurt and sour cream. On a cutting board sprinkle a lot of salt over the garlic and mash with a fork until smooth like a paste. Transfer to the yogurt mixture. In a small bowl, combine the vinegar and sugar, and whisk until the sugar almost dissolves, and add to the yogurt mixture. Stir the mixture and gradually pour in the oil, stirring to combine. Season with salt.
Makes about 3 cups.