The production of ${\mathrm{C}}^{Z+}, {\mathrm{N}}^{Z+}$, and ${\mathrm{O}}^{Z+}$ multicharged atomic ions up to $Z=4$ is investigated using the laser-induced multiple ionization of small molecules in the gas phase in the ${10}^{15}--{10}^{16}\ensuremath{-}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ laser intensity range. For molecules built with a single C, N, or O atom and hydrogen atoms such as ${\mathrm{CH}}_{4}{,\mathrm{ }\mathrm{NH}}_{3}$, and ${\mathrm{H}}_{2}\mathrm{O}$, the $Z=3$ and 4 ion yields are systematically weaker than for molecules built with equivalent atoms such as ${\mathrm{N}}_{2}{,\mathrm{ }\mathrm{C}\mathrm{O},\mathrm{ }\mathrm{O}}_{2}{,\mathrm{ }\mathrm{CO}}_{2}$, and ${\mathrm{N}}_{2}\mathrm{O}$ using rigorously the same laser excitation conditions. In particular, the ${\mathrm{C}}^{4+}{,\mathrm{ }\mathrm{N}}^{4+}$, and ${\mathrm{O}}^{4+}$ ion production efficiency is more than one order of magnitude lower in the first case. In addition, no significant differences are found for the ion production efficiency between diatomic and linear triatomic molecular species built with the same atoms. This overall behavior remains the same at lower laser intensities in the ${10}^{14}--{10}^{15}\ensuremath{-}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$ range for lower atomic ions charge states. The experimental results are in good qualitative agreement with recent theoretical models of molecules in strong laser fields. In order to get quantitative agreement, the initial three-dimensional electronic configuration of each molecule has to be included in nonperturbative theories.