Line a sieve with cheesecloth and spoon in yogurt. Set the sieve over a bowl, leaving at least 1 inch clearance at the bottom. Cover and refrigerate for at least 8 hours or overnight.
Place garlic on a cutting board, sprinkle with salt and mash into a paste with the side of a chef's knife. Transfer to a medium bowl. Add the drained yogurt (discard whey) and whisk until smooth. Stir in feta cheese, oil, parsley and oregano.