Is it possible to run the COFF executable files on UNIX or the ELF executable files on Windows? And what would be the steps to be able to run either file type on Windows and UNIX. I'm just curious.
To actually run executables and have them do useful stuff, you need to worry about the API, not just the executable file format. On a Linux machine with WINE installed, you can run Windows .EXE files from the command line and they do the same thing that they do on Windows.
The other way around is not really possible, however if you install CYGWIN on a Windows machine, and then rebuild the application from source with CYGWIN compilers, you will get an executable that runs on Windows and does the same thing that the Linux executable does on Linux. Lots of standard Linux tools are already ported and in the CYGWIN repository including stuff like X-Windows and GIMP.