Preheat the oven to 450 degrees.
Coat a 9 x 13-inch glass baking dish with cooking spray.
Sprinkle both sides of the halibut fillets with ¼ teaspoon of the salt and the pepper.
In a large skillet over medium-high heat, heat 1 tablespoon of the olive oil. Place fillets in hot oil and sear until browned well, about 2 minutes on each side. Transfer to prepared baking dish.
Add wine to skillet and bring to a boil, scraping up any brown bits. Boil for 1 minute. Add 1 tablespoon of the lemon juice, oregano, remaining 2 tablespoons of olive oil, and ½ teaspoon of the salt, stirring well to mix. Pour wine and lemon sauce over fish and bake for 10 minutes, or until fish flakes easily with a fork.
While fish bakes, return skillet to medium-high heat. Add remaining 1 tablespoon of lemon juice, water, and remaining ¼ teaspoon of salt. Bring to a simmer; add spinach in batches, and cook until just wilted and most of liquid is evaporated.
Divide spinach among 4 serving plates. Top each serving of spinach with a filet.