Heat oil in a medium sauté pan over medium-high heat. Add poblano pepper and onion and sauté for 1 minute, leaving onion crunchy. Season venison strips with salt and pepper, add to pan and sauté for 1 minute, to quickly brown the meat. Add barbecue sauce. Remove from heat and stir in cheese, until incorporated into sauce. Spoon mixture into the center of each tortilla and roll into a cylinder. Keep warm.