What's the most efficient way to kill an Iron Golem? Should I try killing it with sharp pointy things? Should I set up traps to do the work for me?
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:
Carry a bucket of lava. Place lava in the square in which the golem stands, not on the golem directly. Use the bucket to collect the lava once the golem starts to burn to keep the lava from spreading. You may need to apply the lava a few times to finish off the golem.
Note that burning golems can set other things on fire sometimes. I've found this to be uncommon and manageable, but probably also depends on the village. You can extinguish flames that happen to start on buildings.
I've done this in 1.7.2 and it will not generate agro. You can also kill villagers this way without upsetting the golems.