Huginn, Muninn, Heithrun or Saehrimnir will not be immediately seen. They will pop as you progress through the chamber's monsters. Muninn and Saehrimnir will leave behind a message stating "the chamber's stagnant aura has somewhat cleared" if defeated or left to depop respectively.
Huginn may leave behind an Armoury Crate containing various consumable items upon defeat.
Muninn may weaken the enemies upon defeat. A message stating "the creatures lurking in the shadows have calmed" will be received.
Heithrun is the rarest of the four and will double the items in treasure chest after defeating boss.
Saehrimnir may strengthen the enemies if left to despawn. A message stating "the creatures lurking in the shadows have become restless" will be received.