I heartily second the 0000 steel wool, but I'd be really careful about abrasives that might be in powdered cleaners like BarKeepers friend. I think I remember a tale of woe once from a person who used abrasives on the outside of their bowl and it got all hazy.
I know you can use oven cleaner on the outside of the bowl, though. Just try to keep it away from any vent covers, as it will be hard to get off of them (lots and lots of scrubbing with 0000 to follow). If you want to cover the surface, you could put the whole lid or bowl into a construction-sized trash bag, tie it off, and set it in the sun for a couple of hours to work. Or if it's on a smaller-sized surface, you might be able to cover it with a smaller trash bag to keep it moist. In any case, make sure you take off handles and anything else before you bring out the oven cleaner.
I've also had some luck soaking a whole lid and bowl (nestled inside one another) in one of those big rubbermaid storage containers. I haven't used this in conjunction with oven cleaner, however.