How do I improve my Xbox wifi signal?

Most of the WiFi AP manufacturers also sell repeaters. Plug one into an outlet halfway between your AP and your XBox, and, voila!

See this. Yes, to answer a comment, config is required to tell it which SSID to repeat.

Have you looked into PowerLine networking? Assuming your router and XBox are on the same mains circuit in your house, then that should be able to get a wired connection between your rooms without having to mess about laying new wiring. It's also generally better bandwidth and latency than a wireless solution (though not quite up with proper wired ethernet kit).

lots of companies do it these days, a quick Amazon listing for Powerline networking kit has a whole list of them.