GNU Octave for Windows does work on Linux with WINE 1.7.50 at least partially.
Strangely, the command line (CLI) opens up Octave, but hangs upon executing any command (doesn’t work). You can try this by typing in your Linux Terminal (after installing Octave for Windows in WINE)
cd ~/.wine/drive_c/Octave/Octave-4*/bin wine octave.exe --no-gui
However, the GUI does work, but uses 100% of one CPU core for me, even though Octave isn’t doing anything. You can run programs in this mode.
cd ~/.wine/drive_c/Octave/Octave-4*/bin wine octave.exe