Hello,
Essence of Anguish is only useable as WD as your Weapons needs to roll on poison damage to work with this Shard.
Other Classes which can deal poison damage with the Gem of Efficacious Toxin, don’t proc the shard, rendering it almost useless.
Also depending on the Class used, both of them can scale extremely high. Meaning unless its a Shard intended for WD only it needs a fix.
For Example:
a Demonhunter with 5% cooldown reduction gains atleast 75% cooldown reduction, if the shard rolls good this can increase to 125% (by dealing poison damage the cd reduction can increase to 15x + 5% for every enemy hit with poison max 10 stacks so +50% total). The 50% extra damage recieved is neat, but in case of a fix should be increased (my opinion).
Necromancer can use poison-based skills.
It works when the weapon damage is rolled to poison damage.
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I’m playing DH with Essence of Anguish and a weapon that has Poison for the bonus damage range. It works great.
Obviously, it should also work with the poison gem, and probably with poison pets, too.
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My main is the Demon Hunter. And after all these years, it was the Essence of Anguish that made me realize that Demon Hunters DO NOT have a single Skill or associated Rune that does Poison Damage. Only Physical, Lightning, Cold or Fire. 
(I wouldn’t expect them to do Holy or Arcane Damage).
However, StuRedman and Cavendar are right. If you’re going to use the Shards, make sure you reroll any Weapon Damage Range to the Elemental Damage on that Shard. (Normally, you wouldn’t concern yourself with this because it’s just extra Damage).
By the way
Many of the Properties, on any of the Shards, are random. I’ve salvaged many Shards already. I am currently equipping 2 (one in a Helm and one in a Weapon). I have 5 stashed and all are upgraded to the maximum Rank.
These are the Elemental Damages I currently have:
Essence of Anguish = Arcane
Remnant of Pain = Lightning
Stain of Sin = Holy
Dregs of Lies = Holy
Note: I was wrong. The static Property of the Essence of Anguish is always Poison. When I upgraded mine it added Arcane Skills +% Damage. (The Poison trigger was pushed to the bottom of the list of Properties).
My 3 Prime Evil Soul Shards do not have Elemental Damage on them.
So, it will be a lot like the Ethereal Weapons and Primal items. You may find them, but good luck getting the Properties you want or need. 
they used to. There were a couple runes that had poison element, but those were a casualty of the rune/elemental type rebalancing in patch 2.1.0.
We’ve chosen to focus the Demon Hunter more on Cold skills and away from Poison skills. This change allows us to provide more Cold options to the Demon Hunter. Going from five to four elements for the class overall increases the likelihood you’ll get an elemental damage bonus you want.
There also used to be a Poison Hydra rune on wizard.
But in 2.1.0 they balanced most classes to have 4 elements only (except monk with 5 and later necro with 3).
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