Generally speaking, here's my interpretations:
Skirmish triggered by Evaluation Phase (The Voidborn Strikes Back): Resolve the entire Crisis board.
First, Skirmish with 1 Voidborn Fleet Power for each Corruption on your Civilization tracks and Agenda slots
Plus modifiers from the Military Crisis row of the Crisis board
Plus modifiers from applicable Galactic Events (2G & 2H, details further below)
Plus applicable House-specific modifiers
Plus 1 additional Voidborn Fleet Power if this is Cycle 2 or 3 (I believe this is the only time this modifier applies. Rulebook page 33: "Add 1 if the Skirmish is during the Evaluation Phase of Cycle 2 and 3.")
Second, don't forget to resolve the Economy Crisis row of the Crisis board afterwards
Skirmish triggered by Crisis penalty: Resolve a Skirmish only (not the entire Crisis board).
First, Skirmish with 1 Voidborn Fleet Power for each Corruption on your Civilization tracks and Agenda slots
Plus modifiers/effects from the Crisis Card itself (details further below)
Level 1 Cards 10 & 20 (listed as 5 & 15 in TTS, but 10 & 20 in the Glossary)
Level 2 Cards 26, 31 & 35
Level 3 Cards 53, 58, 62, 63, 65 & 67
Plus any modifiers from applicable Galactic Events (2G & 2H, details further below)
Plus applicable House-specific modifiers
Plus modifiers from the Military Crisis row of the Crisis board
Skirmish triggered by War: Resolve the entire Crisis board.
First, Skirmish with 1 Voidborn Fleet Power for each Corruption on your Civilization tracks and Agenda slots
Plus modifiers from the Military Crisis row of the Crisis board
Plus any modifiers/effects from the War Card
Plus any modifiers from applicable Galactic Events (2G & 2H, details further below)
Plus applicable House-specific modifiers
Second, don't forget to resolve the Economy Crisis row of the Crisis board afterwards