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Your main goal here is essentially to gain notoriety with the Exchange if you need it, and gain some experience with the various quests. No part of the Refugee Quad has anything to do with the main quest, however as mentioned before, many of these can help you gain notice, especially taking out or helping out Saquesh at #11.
There are two rival groups here. The Sorrocos on the east side, and the Exchange on the west side. If you break into any container while in eyesight of Exchange Thugs or Serroco's gang, they will attack. In the case of the Exchange, only the immediate witnesses will attack. In Serroco's case, the entire gang will be hostile toward you. In the middle of the quad is the refugee camp where most of the quests are and where I recommend beginning.
1 - Exit
Exit to Refugee Landing Pad (#19).
2 - Exchange Thugs
Both Light Siders and Dark will want to take these two thugs out eventually. When you enter conversation, if you don't have a super high persuade skill, Intimidate them to "draw your weapons and let's do this." After these two are taken out, it will clear the way for Aaida at #4a to reach Lootra, her husband at the docks. If your Intimidate is too high and they let you through, you'll need to kill Visquis later so that all of them become hostile toward you and then take them out.
3 - Geriel, "Plague" Victim
This man has symptoms of the plague and if you use your Treat Injury skill on him, you can heal him for (LS Points) and a reward. Alternatively you can cruelly persuade him to give up and die for (DS Points).
4 - Hussef & Aaida
Talk with Hussef first, and you'll learn of the refugee's ongoing problems with the Serroco Gang and the Exchange. Offer to help out and you'll get the quest to take care of either or both to greatly aid the refugees. As a Dark Side act, you can try to Persuade Hussef that they're all doomed, greatly helping the Exchange and for a chance at a very nice reward from Visquis at #11. I found that it was easiest to do this once you took out the Serroco gang and helped Visquis with Naddaa at #5 and her daughter Adana.
a) Aaida & Lootra:
Near Hussef is Aaida. Talk to her and if you killed the two Exchange Thugs at #2 and have spoken with Lootra at Docks (#7), you can tell her that Lootra lives and that the path is clear for xp and (LS Points).
5 - Naddaa
The Exchange has taken her daughter Adana captive, and is holding her in a cell at #10. Dark Siders with the quest from Saquesh (at #11) to collect her credits and who have not yet rescued Adana can persuade her to sell herself along with her daughter to the Exchange for obvious (DS Points) and Visquis' thanks.
Light Siders will want to hear her story and tell her that you'll try to help. Open the door to #10, fight the Gamorrean guards (if you haven't yet negotiated her release with Visquis), and then talk to Adara. Tell her that you're here to rescue her, and to go back to her mother. When she protests, tell her that you'll take care of Visquis. Then head to Visquis (if you haven't already) and you can Force Persuade or Intimidate him to release Adara... or kill him. That will complete the quest and give you (LS Points).
6 - Kaul
For 20 credits, he'll tell you to enter Stealth mode when looting the containers the Exchange has lying around, in order not to alert the guards.
7 - Kahranna
She's seeking passage off Nar Shaddaa. Dark Siders can pretend you are the spacer she's looking for and collect her credits (persuade for 800, settle on 600), then essentially tell her off for (DS Points). Light Siders can offer to help, and after having been to Goto's Yacht, can see Fassa at Docks (#2) to ask him about passage for Kahranna, to which he will agree, completing the quest.
8 - Odis, Pilot
He's looking for Pilot Work. After you've been to Goto's Yacht, you can talk to Fassa at Docks (#2) on Odis' behalf and he'll agree to help find him a freighter. Alternatively, if you've talked with the Lunar Shadow Crewmen at Docks (#4) but have not yet completed the quest, you can recommend Odis to them, and they'll ditch their captain for (LS Points).
9 - Twi'lek Warning
These two twi'leks will pull you aside to give you a warning about Atton, telling you he's not who he appears. Only if you are able to delve real deep with Atton's troubled past (e.g. having lots of influence with him), will you be able to find more out about this.
10 - Adana
This is where you can find Adana, daughter of Naddaa at #5. If you break in without first talking with Visquis, you will have to fight the nearby Gamorreans. However, the rest of the Exchange will still be non hostile toward you. When you speak with Adana, you can tell her that you are here to rescue her, and subsequently, that you will deal with Visquis if you haven't yet. Tell her to return to her mother. When dealing with Visquis on her behalf at #11, you can Force Persuade or Intimidate him for Adana's release, or kill him.
11 - Saquesh
As the local Exchange boss in this sector, you'll have a few Light Side and Dark Side options with him.
a) Naddaa & Adana:
Dark Siders may wish to ask him if he can use your help, and he'll tell you about the 600 Naddaa owes the Exchange. If you head back to Naddaa and haven't yet released her daughter Adana, you can convince her to sell herself and daughter for (DS Points). Alternatively, if you are looking to help Adana, you can Force Persuade or Intimidate him for her release, or kill him. Killing him will also solve the refugee's Exchange problem, but will make all the remaining Gamorrean thugs hostile to you.
b) The Refugee Problem:
Light Siders will want to Intimidate him to ease up on the Refugees. This will end in a fight, and you'll have all the remaining Exchange thugs on your back as well, which is nothing you cannot easily handle. It will however, earn you (LS Points) and Hussef's thanks. Dark Siders can convince Hussef that they are doomed, come back to Saquesh and when he thanks you, receive a high quality reward. I got perhaps the best blaster rifle in the game, Charric.
12 - Serroco Thug
There's a similar thug on the opposite symmetrical entrance to their territory. He'll stop you and question your reason for being here. You can Force Persuade or Persuade him to let you in, or force your way in, at which point the whole Serroco gang will become hostile toward you. Remember, if you open a container in their territory, they all become aggressive.
13 - Serroco Thugs & Leader
When you talk to their leader, you can try to Persuade him to ease up on the refugees but it will not work. When they are all dead, check out the nearby airspeeder.
14 - Airspeeder
This hunk o' junk can be yours if you found all the necessary pieces and have the required skills. If you manage to repair it, you can have fast transport to any part of Nar Shaddaa, though in reality, it isn't much faster than running, as there are few areas and you'd have to come back to it anyway. But it's kind of cool. You must find these three pieces first and meet the following requirement:
1. Airspeeder Navigation Interface: found at Refugee Landing Pad (#4). Installing it requires the Computer skill.
2. Maneuvering Flaps: found at Docks (#8). Installing it requires the Repair skill.
3. Cryogenic Power Cells: found at Docks (#6). You must complete Lassavou's quest first, and receive them as a reward. Installing them requires the Demolition skill.
4. Finally, you must unlock the Airspeeder controls. This requires the Security skill.
When all requirements are met, you will have your own Airspeeder to putt around in.