A grease fire creates a quick, very intense flash of heat. If the fire is put out quickly, there is a good chance much of the kitchen can be repaired. The most important thing is to clean up the soot and grease as quickly as possible so other parts of the house won't be contaminated, and to ensure full removal of the odor.
Even though the fire occurred in the kitchen, the entire house must be cleaned. Smoke and soot will travel through air ducts and into anything fibrous including furniture, bedding and clothes. Replace the air filter in the furnace and scrub down all parts of the house as quickly as possible. Use dry sponges for cleaning walls and wood paneling. Use vertical motions to clean the soot off of the surface.
In the kitchen, the inside and outside of each cabinet must be wiped down. Clean off as much soot as possible, then sand, reseal and repaint the front of the cabinets to ensure the odor is removed. The cabinets may have to be removed to access the back. Soot and smoke will find their way behind the cabinets and drawers.
As far as food goes, anything that is opened or made of cardboard must be discarded. The toxins from the fire will contaminate these. The only salvageable items are those that are canned.
The fridge is often salvageable. The main concern is the gasket seal on the doors. If those are damaged, you will need to replace the seals or purchase a new refrigerator. If in good working order, be sure to clean the filters, fans and the back of the fridge. Often these will be covered in soot and will infect the food inside the refrigerator.
Many oven ranges have a microwave directly above the stovetop. If your kitchen setup is similar, most likely the microwave will have to be discarded, it is also nearly impossible to remove the odor from the plastic.