Why are prop blades not shaped like household fan blades?
1) Airspeed, 2) Forward motion, 3) Size constraints. Just to begin with.

Household fan blades are extremely slow, so they need more chord to push a meaningful amount of air. Aircraft propellers approach the speed of sound at their tips, and low drag is critical. All things equal, more span and less chord is more efficient. Reducing the airspeed for props has diminishing returns, because aircraft themselves move forward through the air, so a very large propeller adds drag to the aircraft however slow it is. 

In household fans, size constraints are more critical than efficiency. A high-span, low-chord (narrow) blade would be more efficient in a household fan as well - indeed, you can find household fans with such blades. But they have to either spin faster for the same amount of airflow, which adds noise, or be larger in diameter. Ceiling fans, which can be larger, have longer narrower blades than desk or floor-standing fans. 

Ship propellers move in an extremely dense and viscous medium, which changes things even more. The drag of moving through water is extremely high and proportional to V³ power-wise. The thrust force they produce is at most proportional to V², and can be lost to cavitation at high velocity. So their velocity has to be kept as low as possible. The drag cost of adding more chord is also relatively small in water.

On large ships, propellers are already as large as they can be made without sticking out of the water at low draft (on merchant vessels) or reducing the number of shafts that can fit (on combatants). This allows them to spin slower and lose less power to drag.