Soak the cedar planks for at least one hour in warm water. Soak longer, if you have time.
In a shallow dish, stir together the vegetable oil, rice vinegar, sesame oil, soy sauce, green onions, ginger and garlic. Place the salmon fillets in the marinade and turn to coat. Cover and marinate for at least 15 minutes, or up to one hour.
Preheat an outdoor grill for medium heat. Place the planks on the grate. The boards are ready when they start to smoke and crackle just a little.
Place the salmon fillets onto the planks and discard the marinade. Cover, and grill for about 20 minutes. Fish is done when you can flake it with a fork. It will continue to cook after you remove it from the grill.