Festermight: This is by far the best trait for Unholy DK in Battle for Azeroth for both Single Target and AoE! It gains insane value in combination with Infected Claws. Get as many of this as you can, even dropping item level for it can be acceptable in certain situations.
Treacherous Covenant: A very potent flat strength increase while you are above 50% health. If you can guarantee the uptime of this trait it is a very solid Single Target and AoE Option!
Magus of the Dead: A solid Single Target option that got recently buffed in 8.1.5 as a few bugs concerning its behavior got fixed.
Harrowing Decay: Single Target only. Quite a weak option you generally want to avoid this trait.
Cankerous Wounds: Single Target only. Also a weak option that should be avoided.
Bone Spike Graveyard: AoE Trait that should be avoided at all cost. Very weak.
Last Surprise: A very hard trait to play around. Adds a lot of complexity to the spec with a not so great payoff.
Azerite rotation changes
Be more conscious about your wounds and when to pop them. As Festermight has a static 20s duration that cannot be extended, you need to be careful not to pop wounds and/or cooldowns like Apocalypse at the very end of a Festermight window. Generally you want to pool wounds and runes to make sure you can start your next Festermight window strong.
Bone Spike Graveyard
Use Death and Decay on Single Target if you are using this trait
Be mindful of your positioning in relation to your pet and the enemies when using this Trait. You want to hit as many enemies as possible with the chain.
When using this trait your Apocalypse also becomes an AoE cooldown so you might want to think about delaying it so the ghoul explosions will hit the maximum amount of enemies.
Recommended Azerite Traits
3x Festermight = mandatory for every situation.
For Single Target
Helchains or secondary stat increase procs.