What's the most efficient way to kill an Iron Golem?
The Wiki says:
They can take damage from weapons, lava, fire, poison, cacti, and suffocation. They do not take fall damage or drowning damage.
So, I tested.
19 hits from Iron Sword (aprox 19 seconds based on 1 hit/second.)
15 hits from Diamond Sword (aprox 15 seconds based on 1 hit/second.)
13 hits with an arrow. (aprox 26 seconds based on 0.5 hit/second.)
Fire: I dropped a Iron Golem into an enclosed area with a floor on fire. The golem lasted for a good 60 seconds plus before dieing.
Lava: The Iron Golem was dropped into a 1-block deep area of lava. He lasted 13 seconds.
Cacti: Dropped into a pit full of cacti. Around 25 seconds.
Suffocating: Created in a 3x3 hold and then used pistons to squish them in - around 25 seconds.
The verdict is: Using your own default weapons (swords and bows/arrows) are highly effective, and are encouraged. Using lava may be risky; setting up the trap takes time, but just going all out on an Iron Golem should do the trick. Enchantments may also speed up the time it takes to kill one of them.
Like most mobs, the easiest way is suffocation. Once you've captured your golem in a trap, just piston a block into its head and it will die very quickly.
Here's a good tutorial for making such a farm: