All three are similar in that something is being taken that doesn't not belong to the person taking it. There are small differences though.
Loot - Looting typically occurs in a time of social unrest. For example, during a riot or if the police go on strike.
Example - With the police on strike, there was a geat deal of looting taking place.
Rob - This is typically when a person is forced to give up their belongings by another person.
Example - The man was robbed while walking to the store.
Steal - When someone takes something that doesn't belong to them. Typically without the person being aware until after it has happened.
Example - The man steals because he has no job.