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Pour tomatoes and their juice into strainer set over large bowl. Open tomatoes with your hands and remove seeds and fibrous cores; let excess liquid drain from tomatoes, about 5 minutes. Remove ¾ cup tomatoes from strainer and set aside. Set aside 2½ cups tomato juice and discard remainder.
Heat 2 tablespoons oil in 12-inch skillet over medium heat until shimmering. Add onion and cook until softened and lightly browned, 5 to 7 minutes. Stir in garlic and oregano and cook until fragrant, about 30 seconds.
Stir in strained tomatoes and increase heat to medium-high. Cook, stirring often, until liquid has evaporated, tomatoes begin to stick to bottom of skillet, and brown fond forms around pan edges, 10 to 12 minutes. Stir in wine and cook until thick and syrupy, about 1 minute. Stir in reserved tomato juice, scraping up any browned bits. Bring to simmer and cook, stirring occasionally, until sauce is thick, 8 to 10 minutes.
Pulse sauce and reserved tomatoes in food processor until slightly chunky, about 8 pulses. Return sauce to now empty skillet and stir in basil and remaining 1 tablespoon oil. Season with sugar, salt, and pepper to taste before serving.