Decoy (1): Place a target that draw enemies' agro, but it is very easy to die. Most of the time, enemies attack decoy instead of the objective.
Invisibility (2): Longest invisibility ability in the whole game. Perfect for spy missions.
Switch Teleport (3): Swap place between you and allies. This includes your teammates, hostage, and decoy. Many people think this ability is useless, but it's not with augment that make everyone invincible and can't die. [Harrow] can use 4 to make the whole team invincible, but after that he can't use 4 again, making it dangerous for the team. But [Loki] can just keep teleport teammates and make them invincible. You cannot teleport yourself, but you already have invisible.
Radial Disarm (4): Make all enemies with guns to switch to melee. Enemies that already in melee will be staggered for a few seconds. This means enemies with ranged attack like Ancient Healer can still attack you from far away. With augment, enemies will start fighting each others.
Spy mission: Use 2 for invisibility. Decoy (1) then teleport (3) for passing through laser. If you triggered alarm: Use radial disarm (4) with augment on to make the enemies fight each other while you keep moving. If there is only 1 enemy and you can't kill it, Decoy and teleport with augment to make your decoy invincible.
Mobile Defense, Defense, Excavation, and Infested Salvage: Press 1 then 3 while aiming at decoy. Relax and watch the enemies target your decoy and not the objective. If they somehow target the objective, blast them with your radial disarm (with augment) and watch them kill each others.
Survival: There's not much to [Loki] for survival. You can make invincible decoy, force enemies to fight each other, goes invisible and ignore almost all damage. If the enemies are too tough, use radial disarm to make them go melee. Then you should have no trouble dealing with them.
Rescue & Sabotage: Go as fast as you could. Decoy then teleport in a large open area to make things go quicker. In high level missions rescue, teleport the hostage to make them invincible.
Exterminate, Capture, Assassination and [Sanctuary] Onslaught: Just kill
Disruption: You can teleport the Demolyst back so use it to your advantage and help your team.
Defection: Try to teleport everyone to make sure they are safe.
Hijack: Crowd control enemies with radial disarm and invincible decoy. Kill nullifier if there are any.
Bounties in open world: On Cetus, you can teleport hacked fallen drone to the destination. Spy in Fortuna: it's just a spy mission. For protecting Garv in Deimos, make him invincible with your teleport and it's your job to keep him alive. For killing enemies in a circle only (in Deimos), teleport them in the circle if they are taking too long to walk in.
Missions where you don't want to be [Loki]: high level assassination and solo interception.
Combo that you need to get use to: Decoy (1) then Switch Teleport (3) to make decoy invincible. This combo is useful for mobility and create a fake target for the enemies.
In endless mission and arbitration, it is your job to make sure your team is alive. Teleport to whoever almost has their shield down. Your are the team's secondary support. If the mission is in high level, make sure the enemies have no ranged weapons to 1 shot your teammates with your 4. Use 2 to keep you safe and alive.