The Exile's Accord Strangelet is one of two quests that you have to complete in step 9 of The Edge of Fate. This contains the missions Transient and Saturnism, which you'll complete to obtain the Relocator mechanic for use in Kepler, and the Gouge story mission.
This mission takes place in the Exile's Accord region of Kepler, and has you mainly facing Eliksni foes from The House of Exile.
Quest Guide
1. Meet Lodi in the Curtilage Divide within the Exile's Accord

To progress this quest, you'll need to head into the Exile's accord. To do so, head towards it in the map, and you'll end up at a barrier.

Activate the terminal in the barrier to continue on through to meet Lodi.
2. Engage the Exiles to acquire the Relocator tech and the Acceleron held by the Exile commander
Keep heading forward towards the quest marker into the Exile's Accord. Eventually, you'll reach a Matterspark terminal. Activate that and head through the hole at the quest marker. Keep fighting your way through and killing Eliksni. (There's an enemy in a wall that you need to kill, make sure to do this as he will have a waypoint).

Eventually, you'll start killing enemies and picking up an arc buff called 'Conductive Charges'. You need to stand near a pillar (which will have a waypoint), which will let you deposit that buff to charge it up.

Once it's fully charged, head over to the waypoint and destroy the jammer in the room on top of the next waypoint. You'll open a matterspark tunnel, so enter Matterspark and head through the hole.

You'll reach a room with barriers, and a terminal to disable them. Do so. Then, head back out and continue collecting Conductive Charges. Head to the pillar inside of the room and charge it up like the other one.

Once it's charged finish killing ads in the room and make your way to a door (where the ads lead to). You'll find yourself in a room with a final pillar, which you'll also need to charge up.

Once you've done all of this, continue killing ads and head towards the waypoint, until you see a miniboss called Votary Nimis, House Exile Telemechanist.

Kill it, and head back into the center room to find the Eliksni Relocator machine. Activate the machine to summon the Relocator cannon.

Once you've summoned it, pick up the Relocator cannon.

The game will introduce Relocator to you, but essentially, shoot the panels on the wall and then stand in the teleport slot to teleport to the panel that you shot.

There will be a chest outside, so loot it to progress the quest.
3. Meet with Lodi
Follow the waypoint and meet with Lodi. He'll give you your next mission, the Transient mission.
4. Complete the "Transient" Mission
You'll have to complete the Transient mission to progress this quest. Set a waypoint to the mission, and then head to the waypoint; using Matterspark and Relocator to traverse throughout the Exile's Accord. Read our guide below.
5. Locate Lodi in Augur's Bethel
Once you've finished the Transient mission, head to the waypoint to talk to Lodi.
6. Acquire the Acceleron from Spoil and complete the Saturnism mission
This is a two part step, as it requires you to first get the Acceleron from Spoil and then complete the Saturnism mission. To get the acceleron from Spoil, follow the quest checkpoint and keep killing enemies, and eventually you'll be greeted by an encounter in which you have to kill enemies to obtain bombs to throw at pillars to blow them up.
Once you've blown up enough of those pillars, you'll be met by a boss back in this main room. Kill this boss and claim the chest to obtain the Acceleron and access the mission, and then head over to the Saturnism mission to complete it.
Read our guide later in this article on how to solve the Saturnism mission.
7. Destroy the Exiles' Prime Servitor and claim the House's strangelet capsule.
The final step is to complete a mini-mission called "Gouge". It's not listed as a mission like the other two missions in this, but is still a requirement to complete
Transient Mission Guide

Launch into the mission, and head forward into the train.

Once you're out on the other side, head forward through the cave and round following the checkpoint.

Keep fighting your way forward until you reach a laser door.

Grab the Relocator, and shot it into the panel behind the laser door on the left, then step into the portal.

Clear the room and rally up, then disable the barriers.

Run into the room and clear it, and then disable barriers next to the immune door.

A darkness zone will be created, and your job will be to slay out ads and defuse Splinter mines.

Once you've defused the first splinter mine, continue around the room clockwise and defuse the other three mines that spawn, while continuing to clear ads.

Then go into the room, and pick up the Relocator cannon.
Shoot it inside the massive ball, and head in the portal.

Enter Matterspark in that room, and head up to the ramps to either side of the ball to overload the generators on both sides.

Once you've overloaded both generators, shoot the core on the ceiling.

Then, you can leave the room and slay out adds. You'll come up against a boss called Devout Rezilisk, Ramshackle Arcmaster

Saturnism Mission Guide

When you launch into the mission, you'll be launched into a tunnel. Follow your map checkpoint through the tunnel, and jump straight down towards the train below you.

Then, continue through the train, and you'll enter a room with a lot of holes.

Head to the last hole on the right, and go up it.

Activate Matterspark, and then head into the hole, following the path. Eventually you'll find a Relocator, and a jammer at the top of the room.

Destroy the jammer and grab the relocator to drop down the hole where there was previously a shield bubble.

Back in the holes room, head to the last room on the left and shoot the relocator at the panel through the bars, then enter the portal.

Jump down into a room full of shanks, and then continue killing Eliksni adds and following the checkpoint. Eventually, you'll find a Relocator. Grab it, and turn around.

Follow the waypoint, and upgrade the locator. This will give you Relocator II.

Head back to the end of the room, and shoot the pads that link together with the new Relocator cannon, which will bounce the signal. Using one of your normal weapons, shoot the satellite that has the checkpoint on it until its pointing left, then shoot the first in the relay. Then, step on the portal.

You'll teleport into a room with a chest and rally banner. Claim the chest, and then rally up and head through the hole into a darkness zone.

When you enter, clear the room, and then head to the waypoint.

Jump on the pipes down under and head forward, continuing to clear ads.

You'll kill a big Shank called a 'Gravity-Laden Exile' who will drop a cube that you need to pick up.

Once it's up, head back to the waypoint and dunk it into the hole. Then, continue killing ads.

Your waypoint will now lead to a door. Head upstairs and to the Matterspark terminal.

Then, head into the hole on the other side of the room, and follow it round until you drop into a door.

There's another Gravity-Laden Exile. Kill it, then head back with the charge and dunk it like the last.

For the last one, head to the checkpoint. There's an open door, with a room in which you'll need to kill ads.

Once you're at the back of the room, you'll see a Relocator cannon. Head back out and look up.

Shoot the first satellite until it looks like this, and then fire off the Relocator. Then, head into the portal. Head down the hallway and jump down, then kill the last shank and take the charge back to the middle again, and dunk it.

Then, just slay out ads. Eventually, you'll see a miniboss called Ezile Azikk, Dark Matter Foreman. Kill it, and the mission will be over.