As per title: there is a very nice Q&A detailing which of our soldier's skills are unusable when under negative status effects, but what about enemies' abilities?
There's some information in the XCOM-2 Wiki.
It will also cancel overwatch, suppression, mind control, and reanimated corpses if used on the creator of the zombie. [...]
- Mutons cannot counter-attack in melee
- Psionic aliens cannot use any Psi
- Codex can neither teleport nor clone itself
Prevents melee attacks from Rangers, Berserkers, Stun Lancers & Chryssalids (possibly more)
Archons may still melee, even while burning.
Stun Lancers appear to panic, causing them to move randomly and fire their rifle.
Prevents most cooldown-affected abilities, such as Suppression from the Grenadier
Poisoning just damages, & decreases mobility and aim.