Lore: Oblivion never existed, thus he has no lore.
Passive: You can't kill what isn't there. Oblivion is basically invisible and invincible, but at the same moment he can't interact with physical world in any way except his 1st ability.
1. Concept
The viral idea of Oblivion is planted in target enemy's mind, making them manifest warframe into existence and letting him interact with the reality (while still invincible). Target ("Thinker") becomes passive and is targeted by other enemies (Oblivion's health and armor affect thinker's). With thinker's death Oblivion stops to exist again. While thinker is alive, Oblivion accumulates up to 100% additive bonus status chance in 60 seconds. With thinker's death this bonus drops.
Ability doesn't consume energy, but has 20 seconds cooldown.
2. Lethe tides
Oblivion blocks target enemy's memory, making them passively wander around like they were blinded. After affected target's death effect applies to all enemies in range around them. These enemies also share it upon death (chain is infinite). Ability has limited duration, so all affected enemies will return to normal after it ends.
3. No
This can't be happening, right? Oblivion erases all damage received and energy consumed by his allies in the last 5 seconds, which can also revive fallen or dead ones (this also affects the thinker, recovering lost buff counter). If ally was revived, they gain 300% damage buff for a period of time (for thinker's death, Oblivion gains the buff).
Ability has 15 seconds cooldown.
4. Emptiness
Reality tried too hard to erase Oblivion. Thinker and allies affected by "No" spawn at their positions void cracks that suck in all enemies in range. Enemies affected by Lethe Tides get sucked into their own mini-cracks. Getting into the crack deals huge damage to an enemy (if Lethe'd enemy was in another void crack's effect range, they get sucked into it and receive twice as more damage) and stores them in pocket dimension. Attacking the crack will deal increased damage to all enemies inside of it. After a period of time all surviving enemies will return to reality.