Combine 1 cup water and wild rice in a medium saucepan; bring to a boil. Cover, reduce heat, and simmer for 1 hour or until the rice is tender and liquid is absorbed.
Combine 2 cups water and quinoa in a medium saucepan, and bring to a boil. Cover, reduce heat, and simmer 20 minutes or until liquid is absorbed. Remove from heat; fluff with a fork.
Place the rice and quinoa in a large bowl. Stir in the green onions, bell pepper, and cucumber.
Combine oil and remaining ingredients in a small bowl, stirring with a whisk. Drizzle over quinoa mixture; toss gently to coat. Cover and chill at least 2 hours.