Disrupt your opponent's hand, kill their stuff, and fill their graveyard. Curve out into your big creatures and win the game. Easy as that.
Early plays include Chevill, Bane of Monsters to mark your opponent's creatures for death, power through your cards, and gain life to compensate for the life you'll be paying to Thoughtseize, Murderous Rider and your lands. Magmatic Channeler also helps draw through the deck early on, and becomes a big hitter after enough time. Nighthawk Scavenger is your favourite 3-drop and can close the game out quickly if left unchecked, with massive life swings.
Lots of discard between Kroxa, Titan of Death's Hunger, Thoughtseize and Liliana, Waker of the Dead + a full suite of versatile removal should fill up their graveyard and fuel your Nighthawk Scavenger. Two copies of Scavenging Ooze (and more in the sideboard) remove problematic graveyard cards like Uro, Titan of Nature's Wrath and Arclight Phoenix.
Fill your own graveyard with Magmatic Channeler and Fabled Passage. Escape Kroxa to ruin their hand and beat them to death. Your other top end threats to close the game include Glorybringer and Elder Gargaroth, the latter of which helps compensate for life loss with shock/bolt lands and Thoughtseize. Utility includes Vraska, Golgari Queen for blowing up their stuff and accelerating through your deck, and Klothys, God of Destiny for pings.
The mix of graveyard-filling strategies and graveyard hate might seem unintuitive and anti-synergistic at first - why exile your opponent's graveyard with Scavenging Ooze when you have a Nighthawk Scavenger out, or feed your dead creatures to Klothys, God of Destiny when you're trying to escape Kroxa, Titan of Death's Hunger? This is why the graveyard hate pieces are in small numbers - they are there to add utility against the decks where you really need them, or to gain occasional small advantages while keeping the graveyard relatively full. That being said, you do need to be careful with how aggressively you exile with Scavenging Ooze - there's no need to do it against a deck like mono-red when you have a Nighthawk Scavenger on the field, as the lifegain from a pumped-up Scavenger will outweigh that from Ooze. But this is also why Nighthawk Scavenger isn't the only win condition - the deck wins by powering out big creatures, killing your opponent's threats on sight, and disrupting their hand - the graveyard strategy complements this game plan, but isn't the only focus of the deck.
Sideboard
More versatile removal in the form of Assassin's Trophy - switch out a Bloodchief's Thirst and a Heartless Act if facing decks that rely on hard-to-remove utility enchantments or artifacts. Gemrazer also serves this purpose and mutates well onto Scavenging Ooze.
Davriel, Rogue Shadowmage works well against control decks, whose hands you'll want to pull apart. Consider taking out a Klothys, God of Destiny and some removal. Shifting Ceratops does well against blue decks, especially control and the likes of Dimir Rogues. Take out either a Liliana, Waker of the Dead and a Glorybringer or a Magmatic Channeler and an Elder Gargaroth, depending on whether you want to apply extra pressure or control the board (respectively).
One copy of The Eldest Reborn goes far in long, grindy games against control, as well as the second copy of Elder Gargaroth. You can take out a Glorybringer and a Liliana, Waker of the Dead for these two.
Extra graveyard hate includes Grafdigger's Cage and the two extra copies of Scavenging Ooze.
