Nelson Muntz joke withheld for humanitarian reasons (you mention Windows 8.0, Windows 8.1 and Windows Phone in the same sentence). The obvious brute-force solution is running the SDK under Windows 8.0 in a virtual machine, at least until it is updated. The download page http://www.microsoft.com/en-us/download/details.aspx?id=35471 insists on the 64 bit "Professional" variant; are you sure you have the right Windows? Did you use the sdk successfully with Windows 8.0?

The Professional edition of Windows is required only if you wanna run the WP emulator (since it requires and runs only via Microsoft Hyper-V, available only in the Professional edition of Windows 8.x). Although you can try to use another virtual machine to run the phone OS, I really doubt that it will be compatible with Visual Studio.

Under Windows 8.1, you can install WP 8.0 SDK when installing Visual Studio 2013 Professional (actually not available for Express edition). If you want use the Express edition, you must continue to use the 2012 version. For WP 7.x development you must continue to use VS 2012.

If you use a virtual machine beware that the emulator will NOT run since it requires the Microsoft Hypervisor..