We investigate linear and nonlinear transport in a double quantum dot system weakly coupled to spin-polarized leads. In the linear regime, the conductance as well as the nonequilibrium spin accumulation are evaluated in analytic form. The conductance as a function of the gate voltage exhibits four peaks of different heights with mirror symmetry with respect to the charge neutrality point. As the polarization angle is varied, due to exchange effects, the position and shape of the peaks change in a characteristic way, which preserves the electron-hole symmetry of the problem. In the nonlinear regime, various spin-blockade effects are observed. Moreover, negative differential conductance features occur for noncollinear magnetizations of the leads. In the considered sequential tunneling limit, the tunneling magnetoresistance (TMR) is always positive with a characteristic gate voltage dependence for noncollinear magnetization. If a magnetic field is added to the system, the TMR can become negative.