Season the meat on both sides with salt and pepper.
Heat two large skillets on high heat, and add 3 tablespoons of grape seed oil in each. Place the onions, peppers, and mushrooms in one and the oryx meat in the other.
Brown the oryx meat for 3-4 minutes on each side, until no more than medium rare. Remove from the heat and let rest on a cutting board for at least 5 minutes so that the juices retreat back into the meat.
Season the vegetables with salt and pepper and stir. Reduce heat to medium and let them cook for 15-20 minutes until they are completely tender.
To assemble the fajita, slice the oryx meat into thin slices and layer it on a tortilla. Next add a few tablespoons of the vegetables, cilantro, avocado, cheese and a good dose of lime juice. Enjoy!