In a series of two contributions, we present results of our systematic effort in the investigation of organic molecular hyperpolarizabilities using solution-phase dc electric field induced second-harmonic generation (EFISH) and third-harmonic generation (THG) experiments. In the present contribution, the experimental details, theoretical models, and data analysis scheme of a relatively precise and efficient EFISH/THG characterization method are described. Measurement results on donor-acceptor-substituted benzene and stilbene derivatives are presented. Structure-property relationships concerning intrinsic molecular nonlinearities are discussed, including issues concerning the electronic biasing strengths of various donor and acceptor groups, charge-transfer enhancement, substitution pattern, and multiple substituents. Correlations between hyperpolarizability (beta) and substituent constants as well as property trade-off between nonlinearity and optical transparency are established. The observed relations are compared with the prediction of a widely accepted two-state model. The influences of heteroatom and various additional side-group substitutions on hyperpolarizability and the charge-transfer band position are examined. Structural dependencies of the cubic polarizability are also discussed.