The generalized oscillator strengths of the low-lying valence-shell excitations of N2, O2, and C2H2 have been studied by the high-energy electron scattering, the high-resolution inelastic X-ray scattering, and the multireference single- and double-excitation configuration-interaction methods. Good agreement between the present electron-scattering results and the X-ray-scattering ones for the a''1Σg +v'=0 and a''1Σg +v'=1+b1Πuv'=0 excitations of N2 and the A'3Δu excitation of O2 is achieved in the small squared momentum transfer region, while obvious discrepancies among them are observed in the large squared momentum transfer region. This phenomenon indicates that the first Born approximation is satisfied in the small squared momentum transfer region, while it does not hold in the large squared momentum transfer region at an incident electron energy of 1500 eV, in view of the fact that the first Born approximation is satisfied in the X-ray scattering. In addition, the present calculation for the a''1Σg + excitation shows that the traditional assigned v' = 0 and 1 of the a″1Σg + excitation correspond to v' = 9 and 13 of the 21Σg + excitation and reproduces the X-ray-scattering results of the a''1Σg +v'=0 excitation very well except the ones in the small squared momentum transfer region. We also report the generalized oscillator strengths of the à + B̃ excitations of C2H2, and its profile shows that the bending geometry has great influence on the transition feature.