The relative yield excitation functions of neutron-3He elastic cross sections reported in 1982 by the Karlsruhe (Germany) Nuclear Research Center were converted into consistent angle-dependent absolute differential cross sections at 24, 27, and 30 MeV by constructing the elastic cross sections from the total cross sections and the nonelastic cross sections and using them as constraint. This work presents absolute differential cross sections of the elastic and of the two-body nonelastic reactions up to 30 MeV together with reliable estimates of the breakup cross sections. It makes neutron cross-section data of all neutron-3He reactions up to 30 MeV available, expanding the energy range of the data given in Parts I and II.