Measured and calculated positron binding energies are presented for a range of hydrocarbons with up to six carbon atoms (viz., methane, acetylene, ethylene, ethane, propane, butane, and hexane) and their chlorinated counterparts. Both experiment and theory confirm the large effect that the chlorine atoms have on the positron binding energy and the strong sensitivity of the binding energy to the exact position of the chlorine atoms. The experimental binding energies have been obtained by measuring positron resonant annihilation using a trapbased positron beam. The calculations are performed using the previously developed model-correlation-potential method [A. R. Swann and G. F. Gribakin, J. Chem. Phys. 149, 244305 (2018)]. The overall trends are discussed with regard to the molecular polarizability, dipole moment, and geometry. Good agreement between theory and experiment is found, with the exception of the chlorinated ethylenes and chlorinated hexane. Calculations of the electron-positron annihilation rate in the bound state are also presented.