Instructions
Open your Pip-Boy menu and set the "Rescue from Paradise" quest as your active quest. Follow the blip on your radar to walk towards Paradise Falls, where the slaves are being held.
Talk to Grouse, the guard standing outside of Paradise Falls. If you have a low karma score, he will allow you in without question. If your karma score is high, you can bribe him for 500 caps. If not, you will have to enslave someone for him; however, doing so will cause your karma to go down.
Walk to the building called Eulogy's Pad in the southeast area of Paradise Falls. Enter the building and wait for no one to be around so you can steal a few crucial items. You will need the Paradise Falls Box Key located on the table next to the bed, although there are other exclusive items in the building as well, such as the Speech Bobblehead and Eulogy's hat.
Exit the building and walk south to find the slave cages. Do not open the cages. Instead, talk to Squirrel and Sammy, the slaves on your left. Agree to help them escape and you will have multiple options to do so.
Talk to Eulogy and buy each of the slave's freedom for 2,000 caps. If you have a high Speech skill, you can knock the price down to 1,500 caps each. If you don't want to pay him, use the computer terminal in Eulogy's Pad and select the option "Update Network Connections." You need a Science skill of 50 or greater to use the terminal. You can also repair the Junction Box instead. You need a Repair skill of 50 or greater. The Junction Box is found on the northern wall outside of the Food Area, west of Eulogy's Pad.
Talk to Squirrel after you have accessed the terminal or repaired the Junction Box. He will now need you to distract the guard, Forty. Wait until midnight when Forty is alone and talk to him to open up the opportunity to pass a speech check. If you pass, Forty will leave to talk to Eulogy. If you fail, talk to a slave called Crimson and pass the speech check to ask her to keep Forty occupied. If you fail, you can bribe her for 100 caps instead.
Talk to Squirrel after Forty is distracted and all of the slaves besides Penny will escape. Talk to Penny and she will ask you to save another slave named Rory. If you pass a speech check with Penny, you can convince her to leave him behind. If you fail the speech check, walk to the toilet area and find Rory's slave box next to it. Use the key you obtained in Eulogy's Pad to unlock the box and set him free. He may be killed by the slavers as he escapes, but either way you can go back to Penny and she will escape.
Leave Paradise Falls and talk to the slaves outside on the world map. They will now travel back safely to Little Lamplight and you will be allowed access to the town.