If you “move” someone that tends to mean you said or did something that affected them, emotionally. “Touch” can mean the same thing. Sway tends to mean you affected their opinion about something (“I swayed him to my side of the argument”). Reach is a bit more of a stretch, but to copy its relevant Wiktionary definition: “To connect with (someone) on an emotional level, making them receptive of (one); to get through to (someone).”