In a medium bowl, combine softened cream cheese (or yogurt), garlic, lemon juice and oregano. Stir until completely mixed. If using the grated cheese, mix into this layer as well. Spread into bottom of a pie plate or shallow baking dish of approximate size.
Spread the hummus next. Use all of hummus in tub or less to your liking.
In order, create layers of the cucumbers, tomatoes, olives, onion, Feta and basil or parsley.
Cover with plastic wrap and chill at least 4 hours or overnight.
Serve with any combination of the following: Pita chips, fresh vegetables, cut flour tortillas, flatbread or naan.