Warm 1 Tbsp. oil in a skillet over medium-high heat. Pat steak dry; season with salt and pepper. Brown half of steak in a single layer, 1 minute per side. Transfer to a plate. Repeat with remaining oil and steak.
Add mushrooms and onion to same skillet and cook, stirring, until softened, about 7 minutes. Add garlic and sauté for 30 seconds.
Sprinkle flour on top of vegetables. Cook, stirring, for 30 seconds. Add paprika, then slowly stir in juice, Worcestershire and 1½ cups water. Add steak. Bring to a boil, cover and reduce heat to low. Simmer 15 minutes; season with salt and pepper.
Bring a pot of salted water to a boil. Cook noodles for 7 to 8 minutes. Drain. Serve stroganoff over noodles; top with sour cream.