Mix together soy sauce, teriyaki sauce, aji mirin, garlic, and ginger in a large resealable plastic bag. Place pork steaks into marinade, knead several times to coat meat, and squeeze out air. Seal bag and refrigerate for at least 1 hour.
Preheat oven to 350 degrees F (175 degrees C).
Remove pork steaks from marinade and discard used marinade. Place pork steaks into a large baking dish and cover dish with aluminum foil.
Bake in the preheated oven for 30 minutes; uncover dish and bake until juices run clear and an instant-read meat thermometer inserted into the thickest steak reads at least 145 degrees F (65 degrees C), about 10 more minutes.