You can start a PowerShell script from the Windows File Explorer, from the PowerShell scripting environment or from the traditional, DOS-style command line.

The "open" program is specific to OS X and lets you basically drag and drop a file with the -a command onto an application. This way it overrides the per-user OBJ open-with settings.

Open Script Editor (found in Applications > Utilities) and then open your AppleScript app. Run the app within Script Editor and grant any permissions asked for.