Experimental data obtained with a high-resolution transmission experiment are presented for the scattering of electrons in the energy range 20meV-10eV for NH3, 25meV-10eV for H2S, and 15meV-2.5eV for OCS. Data include cross sections for both integral scattering and scattering into the backward hemisphere, the latter up to 650meV impact energy, with an electron energy resolution of between 1.6 and 3.5meV. The new data allow the first detailed comparison with theory for the energy regime dominated by rotationally inelastic and elastic scattering for these species. It is evident that theory still lacks quantitative predictive power at low energy, although qualitative agreement is consistently good for all three species. A discussion is given of the possible presence of a virtual state in OCS scattering as recently proposed on theoretical grounds.