Using a sharp knife, cut feta block into small cubes. Add feta cubes to a small mixing bowl.
Whisk together extra virgin olive oil, lemon juice, sea salt and oregano in a small bowl and drizzle over feta. Allow to marinate while prepping the rest of the ingredients. Marinated feta can be made in advance and stored in the refrigerator for up to 5 days.
On each wooden skewer, layer on a tomato, cucumber slice, black olive, another cucumber slice (if desired), and a feta square.
Serve alongside extra olive oil and oregano. If not serving immediately, store chilled in the refrigerator for up to 3 hours.