Now I don't own oven cleaner and have no plans to own oven cleaner, so I used straight ammonia. If you use ammonia, or even any product containing ammonia please make sure you do not mix it with bleach or any bleach containing products.
Unlike with oven cleaner, ammonia takes longer and requires a little more elbow grease. I soak my rag in ammonia and then lay it on the dirty areas. I also cover it in plastic wrap for at least a few hours. (Overnight is even better.) Don't be like me and wait for a freezing cold day in February when you can't do it outside because you will choke on the fumes. Ask me how I know? :0) I did wear gloves though.
Not perfect, but definitely cleaner than before.