Answer

When a combat occurs involving more than two factions (for example, Chaos, Empire, and a player), the rulebook provides the following guidance:

• Player Units do not enter combat with each other, nor may they share the same hex.
  (Page 32)

• Whenever player Units are in the same hex with Imperial or Chaos Units (or Chaos and Imperial Units are together!), combat occurs.
  (Page 32)

• If your Units enter a hex with any enemy Units, combat begins. If there is an Imperial Garrison or Chaos Skeletons, fight those before fighting any Legion or Horde; if there is more than one Horde, or more than one Legion, fight them in their initiative order from lowest to highest. Each combat counts as a distinct and separate combat, so you can gain Before Combat and After Combat effects multiple times.
  (Page 21)

• When Units of The Empire and Chaos are in the same hex, they begin a combat with each other.
  (Page 44, Page 57)

Combat Order

• If a hex contains player Units, Imperial Units, and Chaos Units:
  • Player Units do not fight each other.
  • Player Units fight Imperial and/or Chaos Units, but not both at once.
  • If both Imperial and Chaos Units are present, they fight each other.
  • If there are multiple enemy types (e.g., Garrison, Legion, Skeletons, Horde), resolve combats in this order:
    • Fight Garrison or Skeletons first.
    • Then fight Legions or Hordes, in initiative order (lowest to highest).

Handling Destroyed Units

• Player Units destroyed go to the Graveyard of The Empire or Chaos, depending on who destroyed them.
• Destroyed Skeletons or Garrisons are placed in the respective Graveyard (Chaos or Empire).
• Legions and Hordes are removed from the game when destroyed, not placed in Graveyards.
• If a Legion destroys a Horde, or vice versa, the winning faction gains the VP.
• After all destroyed Units have been placed in Graveyards, if only enemy Units remain on the hex, they remove any Haven and Defenses there immediately. (Page 36, Page 57)

Summary

• Resolve combats sequentially, not all at once, following the order: Garrison/Skeletons → Legions/Hordes (initiative order).
• Each combat is distinct, and Before/After Combat effects apply to each.
• Destroyed Units are placed in the appropriate Graveyard or removed from the game, as specified.
• Empire and Chaos fight each other if they share a hex, separate from player combats.

Sources:
Page 21, Page 32, Page 36, Page 44, Page 57

Source: Core Rulebook (pp. 21, 32, 36, 44, 57)