Line a strainer with four layers of cheesecloth or one coffee filter and place over a bowl. Place yogurt in prepared strainer; cover yogurt with edges of cheesecloth. Refrigerate for 8 hours or overnight. Remove yogurt from cheesecloth and discard liquid from bowl.
In a large bowl, combine the yogurt, cheese, oil, garlic, parsley, oregano, salt and pepper. Chill until serving. Serve with pita chips and/or vegetables.