The combined effects of the obliqueness and nonextensive electrons are incorporated in the study of ion acoustic (IA) waves in a magnetized plasma. The propagation properties of two possible modes (in the linear regime) are investigated. It is found that the electron nonextensivity decreases the phase velocities of both two modes. Also obliqueness leads to increase of separation between two modes. The nonlinear evolution of IA solitary waves is governed by an energy-like equation. The influence of electron nonextensivity, obliqueness and electron population on the existence domain of solitary waves and the soliton characteristics are examined. It is shown that the existence domain of the IA soliton and its profile is significantly depended on the deviation of electrons from thermodynamic equilibrium and obliqueness. Interestingly, the present model supports compressive as well as rarefactive IA solitary waves. Our finding should elucidate the nonlinear electrostatic structures that propagate in astrophysical and cosmological plasma scenarios where nonextensive and magnetized plasma can exist; like instellar plasma stellar polytropes, solar neutrino problem, peculiar velocities of galaxy clusters, dark-matter halos, protoneutron stars, hadronic matter, quark-gluon plasma, and magnetosphere, etc.
