The Strange-Things Store is a small shop found near the entrance to Facade.
As Fyra stated, it apparently sells "strange things" and its contents are unknown. Even quest related, the shop rarely has any products that the main character can purchase. Many of the items seen in the shop are evidence of the old world, such as the stop signs and surfboards.
The shop can be located on the left side of the city past the Save point in the lower level.