If the only thing you really need is for the URL to be different you can just bind the domains to the same site in IIS. Now keep in mind that everything else must remain the same. If you want to use a different CSS, images, etc. you will have look at building support for multiple sites into your app.
First thing you need to understand how bindings on IIS work. View that
http://blogs.technet.com/b/chrad/archive/2010/01/24/understanding-iis-bindings-websites-virtual-directories-and-lastly-application-pools.aspx[
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Once you have that you can deploy you app to your server. After you setup the web site under IIS you just apply each of URLS you listed about. So every www.customerx would point to the same IIS site.