Combine jicama and lime juice in a large glass bowl and let stand for 20 minutes, stirring every 5 minutes to make sure that all jicama pieces are coated with lime juice. Drain some of the lime juice, depending on your taste.
Mix olive oil and ketchup into the jicama. Stir in tomatoes, onion, and cilantro. Season with oregano, salt, and pepper.
Serve ceviche on tostadas and garnish with avocado.