Why is oven smoking, even after thorough cleaning?

We have a Montgomery Ward gas stove that is at least 30 years old - - ever since the last time we cooked a turkey, it smokes whenever we use the oven - - we have cleaned it thoroughly, removing as many inside panels as we could to clean behind them, but it still smokes - - is there another panel that we don't see? If so, how do we remove it? Could it be something else that is burning besides spills? Is this dangerous?