How do structures in living organisms compare with structures of nonliving things such as construction cranes, buildings, ships, airplanes, or bridges?

For the answer to the question above, there is no such thing as a non-living organism. Because organisms are only a term for living things.

1. Cellular structure: all living organisms generally have a cellular structure i.e., they are made up of one or more cells. 
The protoplasm is the physical basis of life. 

There is no such fundamental and structural unit called cell in non-living things. 

2. metabolism : The various life processes taking place within the body of an organism is collectively termed metabolism. The metabolic processes can occur only in living organisms and not in nonliving things. 

3. growth, repair and death : Growth consists of the living organism absorbing materials entirely different from those that make up its body and convert them into body building substances. Growth in non-living substances such as crystal is at the cost of material similar to that of which it consists. Same substance is added without conversion. 
The growth is permanent, irreversible process in living organisms but can be reversed in non-living things. 
Growth is different in different parts of the body of an organism. Growth is uniform throughout in the non-living things. 

Respiration, nutrition,excretion, movement,irritability, reproduction, life span, death, evolvability are other properties of a living organism.