Empty the freezer's contents. Store frozen food in another freezer, if available. If not, packing it into a separate refrigerator slows thawing. Or pack items into a cooler or coolers with some ice. Do not set the coolers in the sun -- keep them in the kitchen or in an adjoining room that is temperature controlled. You may also use dry ice to keep foods frozen, but always handle it with care. Unplug the freezer. Take out all removable parts, such as the ice bucket and shelves.
Clean the inside of the freezer cabinet with a solution of two tablespoons baking soda in a quart of warm water. You may also add one-fourth cup chlorine bleach to the solution. Use a clean rag and thoroughly wash all the interior surfaces of the freezer. Soak the pieces you took out and scrub them off with the same cleaning solution. Thoroughly clean the rubber seal on the door, as it can absorb and hold odors. Rinse well with fresh water, and dry if needed.
Replace the shelves and ice bucket in the freezer. Spread either baking soda or activated charcoal on cookie sheets and place on the shelves in the freezer. You may be able to find the charcoal at your local appliance store. Plug the freezer back into the outlet, allow the empty freezer to run at its highest setting for two or three days while the burnt smell is absorbed. Other methods include placing open containers of coffee grounds in the freezer, or stuffing crumpled newspaper sprinkled with water between the shelves.
Inspect any visible wiring on the back of the unit for signs of burning, sparking or scorching. Be sure the plug is in good working order and is plugged into the proper outlet. Note any flickering from the light inside the refrigerator, or any sparking or sizzling sounds. These, coupled with a burning odor, can mean trouble, and the unit should be immediately disconnected from the power source until a skilled repairman is available to look at it.