Cut bison skirt steak across the grain into 1-inch wide strips. Place bison strips in a resealable plastic bag set in a shallow bowl.
For marinade, combine oil, lemon juice, lemon zest, the 3 cloves garlic, the 1 teaspoon salt, the oregano, and the ¼ teaspoon pepper in a small bowl. Pour marinade over bison strips. Seal bag; turn to coat bison strips. Marinate in the refrigerator for 2 to 4 hours, turning bag occasionally.
Drain bison strips; discard marinade. Thread bison strips accordion-style onto skewers, trimming as necessary.
For a charcoal or gas grill, place bison skewers on the rack of a covered grill directly over medium heat. Grill for 4 to 6 minutes, turning once halfway through grilling. (Or place skewers on the unheated rack of a broiler pan. Broil for 3 to 4 inches from the heat for 5 to 7 minutes, turning once.) Serve with Yogurt-Cucumber Sauce.