Going for a life drain theme to pay for Erebos's thirsty card draw. Tons of removal, board wipes, and flat-out draining life from other players. Also runs a hefty recursion package to make use of my (and opponents') graveyard.
Game plan:
Early game: hit all of my land drops. If I can ramp out Erebos before turn 4, cool, but it's not really necessary. I just want to get him out on 4 and immediately start drawing a shitload of cards. In the meantime I should have enough removal to discourage aggro strategies, but honestly if I just play Draw-Land-Go for the first 4 turns I'll be happy.
Mid-Game: the goal for the mid game is to abuse the hell out of Erebos to draw my way into one of my big mana doublers or Black Market. By turn 6-7 I hope to have 10+ mana available so I can start pumping out threats while simultaneously using spot removal and board wipes to keep everyone else's boards empty. Now is also the time to try to get some of our big artifacts and enchantments onto the board: Planar Bridge to start dropping big threats every turn, Aetherflux Reservoir to turn the life gain to 11 and maybe give us a 50 damage alpha strike to end the game later, and Mimic Vat to do degenerate things either looping my own ETBs (Gary, etc), or just steal anything nice my opponents may have had. Sheoldred, Blood Artist, Dictate of Erebos, etc also fall into this category - cards that will let me run away with the game if left unchecked, so they're more likely to eat removal and hopefully leave my opponents short of answers when the big game-winning threats start to drop.
Late Game: while everyone else is probably running out of gas, I've got a full hand thanks to Erebos, so I'm just gonna keep drawing as long as I've got the life to do it. By now I should have more Mana and cards than I know what to do with, so I'll just keep playing out big scary demons, wiping the board as necessary, and running through my deck until I hit a wincon - Exsanguinate, Rise of the Dark Realms, etc. It's likely I'll be able to remove a player or two from the game without these first, just using my smaller drain spells and some big beater demons.
Strengths: powerful card draw in the command zone, combined with mono-black's greedy ramp, will make it hard to run out of gas unless I don't hit 4 land drops or Erebos gets stolen. Life gain for me but not for thee prevents the rest of the board from getting out of kill range and makes my little drain spells a lot more painful. Plenty of big demons (and a double helping of removal spells) help me go toe-to-toe with creature-based decks, but I don't need them - I can win even if I can't keep creatures out and have to resort to spellslinging.
Weaknesses: fast combo decks. I mean, that's everyone's weakness really, but it's by far my biggest. Mono-black lacks good answers to artifacts and enchantments. I have the usual colorless options (All is Dust, Scour from Existence, O-stone, Nev's Disk), but they're all pretty expensive and i gotta hope I can draw/tutor them when I need one. Instant-speed answers in general are lacking (unless it's creatures, I can deal with creatures all day). Erebos himself is pretty resilient but if he gets stolen I'm a little low on card draw. And of course being in a mono color, I'm weak to mono-color hate like Blood Moon, Iona, and anything with prot-black.
Notable omissions:
Necropotence - I have this effect (albeit in less efficient form) in the command zone, and I really don't like the downsides of it (discards get exiled, and you don't get the cards until the end step).
Cabal Coffers, Urborg, big money tutors (demonic/vampiric), Damnation, Yawgmoth's Will: too rich for my blood. I'd run them if I had the money but I don't so I won't.
Planeswalkers: I'm running two, there are about 3-4 more that would fit in this deck pretty well (Sorin Markov, a couple more Lilianas, and Karn Liberated). Sorin is too underhanded for my tastes and the rest are just expensive.
Fast ramp (Mana crypt/vault, basalt monolith, etc): again, too expensive, and this deck doesn't really care so much about ramping out early. My commander is pretty cheap and I'm more worried about big late-game ramp than getting ahead of the curve.
Exquisite Blood: I run Sanguine Bond, but I can't bring myself to play this degenerate 2-card combo. It's a shame, too, because both cards are on theme with the deck. If they didn't go infinite together, Blood would probably be about 1/10 its current price and I'd gladly run both.
