Dear Clinton,
It seems that you have installed netcdf manually by setting the option --prefix to /usr/local/netcdf, can you confirm?
Otherwise (i.e. without the prefix option) libnetcdf.so.7 would go to /usr/local/lib (and not /usr/local/netcdf/lib as in your case), as far as I know.
The linker knows about the libraries in /usr/local/lib, but not about /usr/local/netcdf/lib therefore the library is not found.
Does it work when you set in a shell these variables before starting octave?
export PATH=/usr/local/netcdf/bin:$PATH
export LD_LIBRARY_PATH=/usr/local/netcdf/lib:$LD_LIBRARY_PATH
Regards,
Alex