Preheat oven to 425 degrees F (220 degrees C). Line a baking sheet with a piece of aluminum foil and lightly grease.
Peel the turnips, and cut into French fry-sized sticks, about 1/3 by 4 inches. Place into a large bowl, and toss with the vegetable oil to coat. Place the Parmesan cheese, garlic salt, paprika, onion powder in a resealable plastic bag, and shake to mix. Place the oiled turnips into the bag, and shake until evenly coated with the spices. Spread out onto the prepared baking sheet.
Bake in preheated oven until the outside is crispy, and the inside is tender, about 20 minutes. Serve immediately.