In a bowl, mix together the vegetable oil, minced garlic, minced ginger, paprika, cayenne pepper, salt, and pepper to create a marinade.
Rub the marinade all over the meat chunks and let it marinate for at least 1 hour in the refrigerator.
Preheat a grill or barbecue to medium-high heat.
Thread the marinated meat onto skewers.
Grill the meat skewers for about 10-15 minutes, turning occasionally, until the meat is cooked to your desired level of doneness.
Serve the Nyama Choma hot off the grill with lemon wedges on the side if desired.
Enjoy!