With a clean towel pat the tofu dry to remove as much water as possible.
Cut the Tofu into ½ inch thick slices.
In a large shallow dish, mix the rest of the ingredients (olive oil, balsamic vinegar, Dijon mustard, oregano, garlic, salt and pepper to taste) to make the marinade.
Add the tofu to the marinade, turning to coat the tofu well.
Let marinate at least 2 hours or overnight.
Preheat the grill or grill pan to medium-high.
Place the tofu on the grill and cook for about 5 minutes per side, until dark grill marks appear.
Serve with rice and vegetables if desired.