I did a quick search for "server" on the Android marketplace, and most of the results seem to be basic file servers, web servers and FTP servers. These will help with sharing files, using your Android device to store the files, but probably not much else.
Here is one that I found that supports UPnP (Universal Plug n' Play), and DLNA (Digital Living Network Alliance), and is designed for images, video and music, and states that Xbox 360 and PS3 are supported, although it doesn't state that you can use it for games on those consoles, and the screenshots don't seem to have anything about games.
Now I'm assuming that nearly all of these apps will require a network to be in place, that is, all devices would be on Wi-Fi with your router (your homehub or whatever you use for all your devices to connect to the web, assuming you don't have a separate modem), so I don't think that these apps will make your Android like a Wi-Fi hotspot, just a server in the sense of a central machine that stores the data that others use. The actual data connections would be via the router, just all going to/from the Android.