You cannot create a direct Ethernet link between a laptop without an Ethernet port and an Xbox 360. The Xbox 360 requires a network infrastructure (router/switch) or its own Wi-Fi adapter to communicate over IP.
Cheapest Fix: A $15–$20 USB Wi-Fi adapter for the Vaio + a $20–$30 travel router (if no main router) + the Xbox 360's built-in Wi-Fi (S/E models) or a $15 used wireless gaming adapter (for fat 360).