We present a brief account of several recent ab initio nonperturbative studies of very-high- order nonlinear optical processes of diatomic molecular systems in intense ultrashort laser fields with arbitrary molecular orientation. We discuss some recent development of the self-interaction-free time-dependent density functional theoretical (TDDFT) methods with correct long-range asymptotic behavior. The time-dependent Kohn-Sham equations are accurately and efficiently treated by means of the time-dependent generalized pseudospectral (TDGPS) methods in space and time. The procedures are applied to the comprehensive investigation of the multiphoton ionization (MPI) and high-order harmonic generation (HHG) processes of homonuclear (H2, N2, and F2) and heteronuclear (CO, BF, and HF) diatomic molecules in the presence of intense ultrashort laser pulses. Novel high-order nonlinear optical behavior including the electron correlation, multi-orbital effects, orientation- dependence, wavelet time-frequency spectra, and the interfacing of electronic structure with multiphoton dynamics, etc., are presented and discussed in details.