Talk to Mayor MacDaniels inside the Town Hall to receive this quest. You may have defeated some of these homeless people as you're exploring but don't fret since they're already counted even towards the quest progress before you even accept this quest.
1: There's a hidden hobo camp to the west of the Bus Stop. Find the trail behind the tree in the middle of a wooden fence that will lead you to the camp.
2: Inside the U-Stor-It truck.
3: Lot east of Kenny's House
4: Inside the sewers. Can be encountered while doing the quest "Dropping the Kids Off"
5-6: Deeper in the sewers, encountered after you lowered the sewage level.
7: Deeper in the sewers, encountered on your way to the cavern.
After getting rid of the homeless, you can now return to the mayor to complete the quest and add her as your friend.