The option does build a new Nether, but the more important thing is that it applies all new changes to it like Nether fortress with blaze spawner, so you can get these new materials on your old (before updates) world. As you can imagine with a new build, all the buildings/construction you have will be erased.
Overkill requires you to deal 9 hearts of damage, or 18 points of damage, in a single hit. For this answer I will be working in points (half-hearts).
A hit with an iron sword deals 7 damage. A crit multiplies this by 1.5 so it deals 10.5 damage. You need to get another 7.5 points of damage from other effects (enchantment damage isn't multiplied on crits). There are a few ways you could do this.
Sharpness adds 1.25 points of damage per level. Since smite doesn't normally go past rank V, this would only add a maximum of 6 damage, for a total of 16.5. On its own, this won't be enough.
Smite and Bane of Arthropods add 2.5 damage per rank against undead and spiders respectively. 3 ranks would be enough to crit for exactly 18 on an appropriate target. 5 would deal 19.5 damage on a regular hit.
Since Sharpness and Smite/Bane stack, you could combine the two at lower levels. Either Sharpness 4 & Smite/Bane 1 or Sharpness 2 & Smite/Bane 2 would work.
Your other option would be a Strength potion. A strength potion increases your damage by 130%- I can't tell how this stacks with the crit but even in the worse case (additive), you'd deal 7*2.8=19.6 points.
Best Answer
Diamond ore appears in veins of 3-8. As said by the Minecraft wiki and also by personal experience.
Source: Minecraft Wiki