Prepare a grill for direct grilling over medium-high heat (about 400°F). In a medium bowl, combine 1 Tbs. of the oil, 2 Tbs. of the vinegar, a third of the garlic, and the oregano. Add the pork, toss to coat, and let sit at room temperature for 10 minutes.
Meanwhile, in a small bowl, stir together 1 Tbs. of the oil, the remaining garlic, the yogurt, cucumber, lemon juice, 1/4 tsp. salt, and 1/2 tsp. pepper. Set aside. Thread 5 pieces of pork horizontally onto each of four 12-inch metal skewers or soaked wooden skewers, leaving about 1/2 inch of space between pieces. Season the pork with 1/2 tsp. salt. Grill, turning the skewers occasionally, until the pork is well marked and cooked through, 6 to 8 minutes total.
Meanwhile, in a large bowl, toss the greens, tomatoes, and feta with the remaining 1 Tbs. vinegar, then with 1/4 tsp. salt, 1/8 tsp. pepper, and the remaining 2 Tbs. oil. Arrange the salad on plates or a serving platter. Lay the pork skewers on top, spoon some of the tzatziki over the pork, and serve with the remaining tzatziki on the side.
To round out the meal, serve toasted pita alongside.