This is a different take on the Warlock questline than most decks: instead of trying to complete the quest as fast as possible, we complete it eventually and kill the opponent the same turn or the turn after. The key card here is Stealer of Souls: with a lot of card draw and expensive demons in the deck, the damage adds up very quickly.

I've only played a handful of games so far, but it feels pretty powerful.

Game Plan

In the early turns, try to stay healthy and improve your hand by drawing and discounting cards. Also spend your mana to dump cards that are not useful in your current matchup, since hand size can become an issue in the late game. You don't need to hurry the quest progression: use Unstable Shadow Blast for removing high-health minions, for example.

Once you have Stealer of Souls, some card draw and enough mana, you can go for a big turn in which you complete the quest and deal lots of damage to your opponent. If you are close to fatigue, this is probably enough to OTK them. If not, you should be able to at least build a big board of demons that will keep you safe until the next turn.

Mechanics

Be aware that when you kill off Gadgetzan Auctioneer with a spell, he draws before dying and before the quest completion is checked. I once milled my quest reward that way.

As with all the questlines, progression does not wrap around when going into the next phase, so take care to order your self-damage effects to minimize progress lost on phase transitions.

Mulligan

If you're up against a deck that takes the board early, keep removal and Tamsin Roame.

Against slow or spell-heavy decks, keep Stealer of Souls and card draw.

Demonic Studies is a decent keep as well, since it allows you to play Stealer of Souls earlier, and sometimes even discovers another one.

Raise Dead can be a keep if you already found Tamsin or Stealer of Souls.

Replacements

The Demon Seed is essential; if you're missing it but still would like to play Stealer of Souls, I suggest trying this deck instead.

Tamsin Roame is very useful at keeping you alive and if you don't need to play the zero-cost spells early you can use them to fuel Gadgetzan Auctioneer. If you have to replace her, put in removal or healing instead. With Mage still being quite popular, healing is probably more useful, for example Spice Bread Baker. I'm not sure if it's worth running two copies of Siphon Soul without Tamsin; if they end up being too clunky, maybe replace one of those as well.

Mortal Coil is the weakest of the spells, so take that out if you need a slot for a tech card like Rustrot Viper.