How much sun is the plant getting? What are the temperatures like where you are? What variety of oregano is it? Some varieties produce red leaves? Other than the color, the leaves look perfectly healthy to me and if they taste ok then I don't see any reason not to eat them. Pinching off the red tips will also encourage new green growth. If it is not a red variety then the plant is probably stressed in some way - light, temperature, nutrients etc. A little more information on growing conditions and how you care for the plant would be helpful.