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Nowadays, there has been a great deal of interest in understanding different types of wave propagation in dusty plasmas. The nonlinear propagation of ion acoustic (IA), dust-ion acoustic (DIA), and dust-acoustic (DA) solitary waves (SWs) in a magnetized dusty plasma are studied theoretically by taking into account the effect of the nonextensive electrons and the external magnetic field. The Korteweg de-Vries (K-dV) equation for these small but finite amplitude SWs are derived and their obliqueness are studied by the reductive perturbation method. The dust, ions, nonextensive electrons, the external magnetic field, and the angle between the direction of propagation and the magnetic field significantly modify the basic features of the SWs. The number density and mass of the extremely massive negatively charged dust grain modify the basic properties of the SWs. The SWs exhibit compression and rarefaction depending on the nonextensive parameter of electrons. The implications of the underlying physics of the obtained results, which are relevant to space plasmas (e.g. Earth's bow-shock, hadronic matter, etc.) and laboratory plasmas (e.g. rf discharges, etc.), are also analyzed.