Combine all marinade ingredients in a large bowl and mix well. Add venison and toss well. Transfer to a large resealable plastic bag and marinate in the refrigerator for 6 to 8 hours.
Remove the venison from the marinade. Heat the oil in heavy cast-iron skillet. Add the drained venison strips and sear for 3 to 4 minutes. Remove the venison from the pan. Place cooked strips in a single layer on 6 tortillas, cover with a mixture of both cheeses, and add another tortilla as a cover. Carefully transfer the quesadilla into the skillet, pressing down slightly with a spatula to ensure maximum contact. Cook for 20 to 30 seconds per side, using caution when flipping over. Slice into 6 wedges with a pizza cutter and top with you favorite sauce.