Whisk teriyaki sauce, water, barbeque sauce, honey, Cajun seasoning, salt, garlic, and onion powder together in a bowl. Reserve 1/4 cup of the marinade in a small bowl and pour rest into a large resealable plastic bag. Add steaks to the bag. Squeeze bag to remove as much air as possible, while assuring meat is covered completely in marinade, and seal.
Refrigerate reserved marinade and marinate steaks in the refrigerator, 8 hours to overnight.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove steaks from the marinade and shake to remove excess moisture from meat. Discard used marinade.
Grill steaks, basting frequently with reserved marinade, until they are beginning to firm and are hot and slightly pink in the center, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C).