Space plasmas are often observed to contain more particles in the high-energy tail than the usual Maxwellian distributions, and are well modeled by kappa distributions. The hybrid kappa-Maxwellian distribution and associated generalized plasma dispersion function Z(kappa M) were recently introduced to model magnetized space plasmas. The susceptibility tensor for a kappa-Maxwellian plasma component is derived, making use of Z(kappa M). This enables one to make general studies of obliquely propagating electromagnetic waves in a magnetoplasma. The susceptibility and dielectric tensors reduce to the Maxwellian expressions in the limit kappa ->infinity. As an illustration, the formalism is applied to the lower branch of the R mode and its off-parallel variant. For low kappa values, low-wavenumber, low-frequency parallel whistler waves are shown to be stable, unlike the Maxwellian case, which is unstable if the perpendicular temperature exceeds the parallel temperature. A numerical study is made of the effects of the value of kappa, the propagation angle, and the temperature anisotropy ratio on dispersion and damping. The kappa-Maxwellian distribution with very low kappa is found to be unstable in an overdense plasma near the electron-cyclotron frequency even when the parallel and perpendicular temperatures are equal, because of the anisotropy of the contours in velocity space.