The physical properties of the nematic phases formed by four bent-core oxadiazole based materials are reported. In particular, the splay (K11), twist (K22) and bend (K33) elastic constants, the birefringence and the dielectric anisotropy of the materials are described and the effect of chain length and the presence of fluoro-substituents at the outer phenylene group of the aromatic core structure on these parameters is determined. The birefringence and order parameter are found to be independent of the modification of molecular structure. The dielectric anisotropy is quite strongly dependent on molecular structure; the fluoro-substituted material has the largest magnitude of dielectric anisotropy while the alkyl-substituted compound has the smallest. Changes in the molecular length and fluoro-substitution in the bent-core materials are found to have little influence on the splay, twist and bend elastic constants at equivalent reduced temperatures. However, the material substituted with an alkyl terminal chain exhibits both smaller elastic constants and a less marked dependence on temperature than the alkoxy-substituted compounds. A possible insight into the behaviour of the elastic constants relevant to the formation of the dark conglomerate phase, which underlies the nematic phase in one of the compounds studied, is suggested by following the analysis proposed by Berreman and Meiboom. Importantly, using molecular field theory and atomistic modelling, we calculate elastic constants that are in excellent agreement with the experimental values. Our conclusion that the elasticity in the nematic phase formed from bent-core molecules is not strongly influenced by changes to the terminal chains or the presence of fluoro-substituents at the outer phenylene group of the aromatic core structure is in agreement with our previous work showing that the dominant parameter is the bend angle.