Word for "stealing things during natural disasters"

Looting. See the Wikipedia article on Looting, specifically in cases of catastrophe, sense (1) natural disaster.

Quoting from Wikipedia:

Looting, also referred to as sacking, ransacking, plundering, despoiling, despoliation, and pillaging, is the indiscriminate taking of goods by force as part of a military or political victory, or during a catastrophe, such as war, natural disaster, or rioting. The term is also used in a broader sense to describe egregious instances of theft and embezzlement, such as the "plundering" of private or public assets by governments. Looting is loosely distinguished from scavenging in terms of objects taken: scavenging implies taking of essential items such as food, water, shelter, or other material needed for survival while looting implies items not necessary for survival such as luxury goods, art work, precious metals or other assorted items of value to the looters. The proceeds of all these activities can be described as loot, plunder, spoils, or pillage.

Looting during a riot or a natural disaster is deemed a despicable act and historically (as recently as the 2005 hurricane Katrina in New Orleans) in the United States there have been occasions when it has been sanctioned for police or even civilians to "shoot looters on sight." See http://www.volokh.com/posts/1125599174.shtml

Looting is the correct word. Plunder and pillage are used with looting for forced illegal acts in war and conflict. Looting is the only one of the three words commonly used for theft in natural disasters.

Pillage: To rob of goods by force, especially in time of war; plunder. To take as spoils.

Plunder: To rob of goods by force, especially in time of war; pillage: plunder a village. To seize wrongfully or by force; steal: plundered the supplies.

I believe these best match you definition, but they're both rather dramatic for conversation- they're more likely to be used in news videos or articles. If two men were thinking about robbing a store, taking advantage of a natural disaster, I believe they would likely use words like loot, rob, ransack, sack, steal from, etc.