Heat oil in a large skillet over medium-high heat; add garlic and sauté 1 minute. Add oregano and stir to coat. Add shrimp and sauté until bright pink, stirring frequently, about 3 minutes. Add wine and simmer about 1 minute.
Dissolve cornstarch in chicken broth in a small cup and whisk until blended; add mixture to skillet and simmer 2 minutes, until sauce thickens. Season to taste with salt and pepper.
Transfer cooked linguini to four individual shallow bowls and spoon shrimp and sauce over top; sprinkle with parsley and basil. Yields about 1 1/3 cups of pasta, 1/4 cup of sauce and 3 ounces of shrimp per serving.