Overdrive/Altairian

Firestorm Overdrive
The Firestorm Overdrive is exclusive to the Bastion Cruiser and Blackguard Cruiser. Upon complete shield depletion, a massive rush of energy enhances the damage, shield bypass and range of the ship's weaponry for a short period of time.

Barrage Overdrive
The Barrage Overdrive is exclusive to the Paragon Battleship and Kingpin Battleship. While there is an enemy (not including squadrons) in any of its attack arcs, weapons have increased AoE radius, projectile speed, and turning speed, with the bonus lasting up to 3 seconds after the pre-condition is no longer satisfied.

Catalyst Overdrive
The Catalyst Overdrive is exclusive to the Cavalier Cutter and Assassin Cutter. Whenever the ship is affected by Stasis Dealing effects (except for Stasis Field), it gains increased forward speed, shield defense, instant shield regeneration and stasis resistance for a brief period. The shield buffs do not apply if shields are fully depleted. Do note that a stasis resistance of over 100% will reverse the effects of Stasis.

Ballista Overdrive
The Ballista Overdrive is exclusive to the Inquisitor Destroyer and Saboteur Destroyer. After the ship goes through sufficient Firing Cycles (calculated across all equipped weapons), its Driver weapons have additional wall piercing, regular piercing as well as projectile range for 3 seconds, starting when the next shot is fired.

Enguard Overdrive
When 3 or more enemies are within the targeting arc, a Sovereign Carrier with the Enguard Overdrive Generator (or a Usurper Carrier with the Shirk Overdrive Generator) gains boosts to Counter Chain, Counter Pierce, Shield Defense, as well as the ability to recharge its shields instantaneously. In addition, the Enguard Field is generated around the carrier.

The effects last until 3 seconds after the condition is no longer satisfied.

Riposte Overdrive
When a Sovereign Carrier with the Riposte Overdrive Generator takes 2,500 points of health damage, it gains the ability to recharge its shields even when under fire, at an increased rate. This can be triggered multiple times; however, only health damage taken while the Overdrive is inactive count towards the requirement. In addition, the Riposte Field is generated around the carrier.

The effects last for 3 seconds. The timer will not reset even if the Sovereign Carrier takes another 2,500 health damage during this period.

Feedback Loop
The Feedback Loop is exclusive to the Renascence Battlecruiser. When the threshold of DoT Stacks is reached (calculated each time they "tick"), it briefly gains the ability to apply a lengthy debuff to Phase Charge Rate as well as speed to enemies on hit, while simultaneously boosting its own shields and increasing its maneuverability and resistance against Plasma Damage.

The effects last until 3 seconds after the condition is no longer satisfied.

Smite
Smite is exclusive to the Zeus. When it takes a certain amount of damage to its health, its Cannon weapons and Ricochet abilities are boosted, and its shields are strengthened for a short period of time.

Unite
Unite is exclusive to the Orator Dreadnought. When it takes a certain amount of damage to its shields, its spawned ships are boosted for a long period of time. This overdrive can be refreshed while active.

Breakpoint
Breakpoint is exclusive to the Orator Dreadnought. When a certain amount of spawned ships are lost, the Orator becomes more durable and manueverable for a long period of time.

Savior
Savior is exclusive to the Ajax. When a friendly ship within maximum weapon range loses its shields, the Savior Field is activated for a short period of time which redirects incoming hits to the Ajax. During this period, the Ajax also receives some defensive bonuses.

Fortify
Fortify is exclusive to the Ajax. When it takes a significant amount of shield damage, the hull and its shield briefly gains immunity to most types of damage but is almost completely unable to move during that period (ignores stasis resist).

Swift
Swift is exclusive to the Orion. Whenever it takes a small amount of shield damage, the hull gains a huge bonus to speed, immunity to Plasma damage, as well as an array of offensive bonuses, for a short period of time. Note that this overdrive can be refreshed while active.

Hunt
Hunt is exclusive to the Artemis. Whenever it deals a moderate amount of health damage, it launches a drone that looks exactly like the Fury Drone for an extended period of time. The drone deals Alien damage and applies a moderate Phase Hacked debuff. Note that this overdrive cannot be refreshed until its full duration of 20 seconds has passed.

Vengeance
Vengeance is exclusive to the Artemis. Whenever the squadron launched from the Hunt overdrive is taken out of combat (either due to it being destroyed, or having been returned to your ship after its flight time expires), for 10 seconds, the Artemis gains a minor weapon and ship speed boost, as well as the ability to apply the Weapon Disrupted debuff (the debuff lasts for 2 weapon cycles as its duration is unspecified). Note that the squadron is, regardless, unable to apply Weapon Disruption.

Lex Talionis
Lex Talionis is exclusive to the Ancient Reaper. When a certain amount of spawned ships are lost, the Ancient Reaper deals more damage and becomes more manueverable for a moderate period of time.

Reaper Onslaught
Reaper Onslaught is exclusive to the Ancient Reaper. When it deals enough health damage, it activates its spawners so that they can spawn in Alien Reapers for a long period of time. When the overdrive ends, the spawned ships are immediately destroyed, and the counter can be filled once again.

Note that unlike regular spawners, the defensive and offensive ranges are 5 km and 12 km respectively.

Reckoning
Reckoning is exclusive to the Imperator Dreadnought. Whenever the dreadnought takes a significant amount of shield damage, it strengthens its shields to provide total defense and regenerate the lost energy, in addition to boosting the ship's turning speed, for a short duration.

Assailment
Assailment is exclusive to the Imperator Dreadnought. When either the Skirmisher Squad, Disruption Squad or Guardian Squad is physically returned to the ship (either due to being destroyed or running out of fuel), it receives a bonus to damage and weapon speed, in addition to the ability to apply the Weapon Disrupted debuff. This overdrive can be stacked up to 3 times.

Skirmisher Squad
Skirmisher Squad is exclusive to the Imperator Dreadnought. It is a long-range squadron that is launched while at least one enemy ship or module remains inside the ship's weapon arc (not hangar arc), up to 5 seconds thereafter. The squadron appears as a golden Gladiator Swarm and deals heavy Alien damage but is relatively fragile. (Does not apply phase hacking.)

Even after the overdrive ends, the squadron remains active for the rest of its flight time.

Disruption Squad
Disruption Squad is exclusive to the Imperator Dreadnought. It is a long-range squadron that is launched while at least two enemy ships or modules remain inside the ship's weapon arc (not hangar arc), up to 5 seconds thereafter. The squadron appears as a golden Charger Swarm has mediocre Explosive damage output and health, but applies the Weapon Disrupted and the Phase Charge Hacked debuffs.

Even after the overdrive ends, the squadron remains active for the rest of its flight time.

Guardian Squad
Guardian Squad is exclusive to the Imperator Dreadnought. It is a long-range squadron that is launched while at least three enemy ships or modules remain inside the ship's weapon arc (not hangar arc), up to 5 seconds thereafter. The squadron appears as a golden Ranger Swarm has low Kinetic DPS but is tough to destroy. (Does not apply phase hacking.)

Even after the overdrive ends, the squadron remains active for the rest of its flight time.

Trivia

 * The range bonus of the Firestorm Overdrive was decreased from +40% to +20% during a balancing patch in April 2018.
 * The Surge Core PL was originally considered as an item, the Pulsar Charger. It was first seen in Altairian Mothership Fleets.
 * The Feedback Loop overdrive was buffed in the early May 2019 update, as mentioned here.
 * The Orator Dreadnought's stats were inadvertently released in the late June 2019 update through unlocked crafting recipes when logging in through the mobile version. While this was quickly discovered and fixed, players who have already unlocked the recipe can continue viewing the ship's stats. When the ship was officially released in the late July 2019 update, its stats and overdrives received massive buffs.
 * The Ajax originally suffered from a bug in which its Fortify overdrive granted resistance to all damage to its shields (including Blight and Void). This was fixed in the late December 2019 update, which also changed the Fortify overdrive to provide hull resistance in addition to shield resistance.
 * The Hunt overdrive complements the Artemis' namesake, the Greek goddess of the hunt.
 * Originally, the Hunt overdrive can begin to refresh once the squadron is ready to be launched again (e.g. in case it was prematurely destroyed). However, after the late May 2020 update, it was changed such that the full duration of 20 seconds has to pass before it can do so.
 * Originally, Savior could be activated by losing Ablative Armor. This has been no longer the case since the late July 2020 update.
 * The Barrage overdrive received a buff after the late March 2020 update which allowed its overdrive to activate when an enemy is only in one firing arc (down from two). However, its description was not updated until the late July 2020 update, causing players to believe that it was a bug.