If one of Shroud of Silent Mists lands is targeted with Vengeance of the Dead and Invaders have their Health boosted by an Event, when damaged Invaders die at the end of the turn when the health boost wears off, do you get the benefit of Vengeance of the Dead?

If one of Shroud of Silent Mists lands is targeted with Vengeance of the Dead and Invaders have their Health boosted by an Event, when damaged Invaders die at the end of the turn when the health boost wears off, do you get the benefit of Vengeance of the Dead?

No.
The effect of Vengeance of the Dead (extra Damage when Towns/Cities are Destroyed) and the Health boost wear off at the same time in Time Passes, so you don't get the extra Damage. (Health bonuses also wear off during Time Passes, so you need Shroud of Silent Mists to prevent the healing for the Invaders to actually die.)
Similar comments apply to other effects that wear off at the end of the turn.