[Scoobert2000]

• Awaken State
  

They should't have a grey cloud/"fire" surrounding the character, they may end up using it when they are about to get hit from a Super Attack/Low on Health/etc.
If your playing as a Investigator or Quinxs, throw a CRc Gas. This will suppress the Ghoul's Awaken State

• Rampage
  

This tends to happen when they are suppose to die, the chances of getting Rampage is rare though.
CRc Gas cannot suppress a Rampage State
However they can still take damage from Flame attack, if they do not put out the flame in time they can die during a Rampage, or from "Respawn Penalty"

[Jotaku]

Oh I didn't realize there was gas thing when in awaken state, Thanks!