You might remember a video I made about a T6 rift clear in 44 seconds, which hyped many to play the "WW DH" in patch 2.2. Now, here is the guide to the build I used.
The general idea is to use Strafe to reset your cooldown of Rain of Vengeance, thus buffing your dps like crazy, and moving at insane speeds at the same time. With Smoke Screen - Displacement, Tactical Advantage, Boon of the Hoarder, Warzechian Armguards, etc. you can easily assume a permanent 150-250% movement speed bonus. The good thing about the Natalya set is that it increases all of your dps, including all of your skills, gems and conduit. It does not have a totally fixed item or skill setup, so you can experiment a lot with it to see what fits you best.
This build's purpose is only to farm T6 or low GRs effficiently, and not to push the rankings. In order to make Natalya's work for the latter, you have to come up with other builds. However, with some adjustments a Strafe Natalya build should be able to push into the 50s.
For some gameplay footage, consider watching the video. I've included a timeline in the description to let you jump to different parts quickly.
Generally, you will want to use Natalya's Slayer and Calamity. The weapon with the highest damage per attack should be in your mainhand (left slot), as the Rain of Vengeance damage only takes this one into account. The other weapon should preferably have RCR and CDR (or maybe Bonus to Elites). You should also stack a little bit of toughness, the best spot is vitality on the helm, as Strafe bonus is not doing that much anyway. If you feel like you are dying to quickly, consider to also get vitality on your chest and possibly gloves or weapons.
For the different options to consider, see the item section above. Since there are not enough choices to add, I will also throw these items in: Profane Pauldrons, Sash of Knives, Convention of Elements, any immunity amulet. The general gearing strategy is to get enough RCR and CDR to get perma Strafe + perma RoV to work. With low paragon this might be a little bit difficult, but the build is really strong in T6, so with some less damage you should still be able to farm the lower torments very efficiently until you have good rolls on most of your items. Your gearing choices also depend a lot on your strategy, e.g. if you want to trade a few seconds here and there to pick up globes, you can also drop Avarice Band + Boon of the Hoarder and use other options, or if you really can't get any RCR items, you could go RoRG and add both Pride's Fall and Hexing Pants for lots of resources.
As for the amulets, I recommend using a Hellfire once you feel comfortable without an immunity amulet. Good choices for a 5th passive are: Hot Pursuit, Awareness, Sharpshooter or Single Out (for GRs).
The skill setup above requires you to use either Rain of Vengeance or Strafe on your left mouse button, so you will have to use force attack to activate them. If you don't want to do this, you could consider swapping Vengeance with Shuriken Cloud to passively boost your dps a little. Shuriken Cloud can be used on left moust button as well and this lets you put both Rain of Vengeance on other (and more convenient) slots. In general, Dark Cloud is the preferred rune to use for Rain of Vengeance because it follows you around as you move, however you could also consider Shade with it's huge AoE. The rune choice in Strafe is not really relevant because most of your damage will come from RoV, so I suggest to just use Drifting Shadow if you are not using a K'mar Tenclip. In case you do, Icy Trail or Demolition are good options.
For speed GRs, you should change a couple of items (see above). In general, you have to adapt to your party composition and clear speed, you can trade RCR for CDR or more damage if you feel like you're getting enough health globes, and also stack some more toughness because you might be a little squishy in tier 35-40. You should also try to let others soak the damage and not run in first, so keep an eye out for your supporters.
[Update 25 April 2015]
With some more experimentation going into this build recently, a few things have changed. If you are getting close to the high-end, it seems even better to use Focus and Restraint and drop any resource items altogether. Drop Vengeance / Chakram and use Evasive Fire - Focus. I recently shared my contribution to the T6 Rift Clearing Competition and managed to complete 10 runs in 21min and 17sec. I also used Wreath of Lightning instead of another dps gem, the damage boost from the rings is more than enough, I wasn't even using a Hellfire amulet and only had one ancient weapon. This build is strong enough to solo farm rifts in 4-player parties at almost the same speed (maybe +10 seconds per run), e.g.while the other party members are clearing bounties and just leech the RG in your rift. The same applies to speedfarming GRs, where you would still want to use Crashing Rain and some more toughness, but if you get your timing on Smoke Screen right, you should be able to survive up until tier 45 pretty well, at least a lot better than with the Unhallowed Essence builds.