Yes, your LEDs can be powered from the "outlet" and your Arduino can be powered from the PC via USB.
By "outlet" I assume you mean a regulated AC-DC power supply, and you do not mean to power your LEDs directly with 120 or 240VAC.
For more detailed advice, you must provide more detail about your components and your idea. Read the forum guide in the sticky post and try to follow it the best you can, even if you don't yet have some of the things it asks for.