Removing burnt olive oil from an enamelled cast iron pan and a non-stick marble pan?
Lodge has a pretty extensive, instructions for usage and caring for enamel cast iron pans. 

In short the advice is as follows:


Hand washing with warm soapy water and a nylon Scrub Brush is recommended to preserve the cookware’s original appearance. Citrus juices and citrus-based cleaners (including some dishwasher detergents) should not be used, as they can dull the exterior gloss. 
If necessary, use nylon pads or scrapers to remove food residue; metal pads or utensils will scratch or chip porcelain.
Remove slight stains by rubbing with dampened cloth and commercial Enamel Cleaner product or other ceramic cleaner according to directions on bottle.
For persistent stains, soak interior of the cookware for 2 to 3 hours with a mixture of 3 tablespoons of household bleach per quart of water.
To remove stubborn baked on food, bring to a boil 2 cups of water and 4 tablespoons of baking soda. Boil for a few minutes then use a Pan Scraper to loosen food.