Oriented external electric fields (OEEFs) have been shown to have great potential in being able to provide unprecedented control of chemical reactions, catalysis, and selectivity with applications ranging from H-2 storage to molecular machines. We report a theoretical study of the atomic origins of molecular changes because of OEEFs since understanding the characteristics of OEEF-induced couplings between atomic and molecular properties is an important step toward comprehensive understanding of the effects of strong external fields on the molecular structure, stability, and reactivity. We focus on the atomic and molecular (bond) properties of a set of homo- (H-2, N-2, O-2, F-2, and Cl-2) and heterodiatomic (HF, HCl, CO, and NO) molecules under intense external electric fields in the context of quantum theory of atoms in molecules (QTAIM). It is shown that the atomic properties (atomic charges, energies, and localization indices) correlate linearly with the field strengths, but molecular properties (bond length, electron density at the bond critical point, and electron delocalization index) exhibit nonlinear responses to the imposed fields. In particular, the changes in the electron density distribution alter the shapes and locations of the zero-flux surfaces, atomic volumes, atomic electron population, and localization/delocalization indices. The topography and topology of the molecular electrostatic potential undergo dramatic changes. External fields also perturb the covalent-polar-ionic characteristic of the studied chemical bonds, hallmarking the impact of electric fields on the stability and reactivity of chemical compounds. The findings are well-rationalized within the framework of the QTAIM and form a coherent conceptual understanding of these effects in prototypical diatomic molecules.