The most popular modeling approach for dielectrophoresis (DEP) is the effective multipole (EM) method. It approximates the polarization-induced charge distribution in an object of interest by a set of multipolar moments. The Coulombic interaction of these moments with the external polarizing electric field then gives the DEP force and torque acting on the object. The multipolar moments for objects placed in arbitrary harmonic electric fields are, however, known only for spherical objects. This shape restriction significantly limits the use of the EM method. We present an approach for online (in real time) computation of multipolar moments for objects of arbitrary shapes having even arbitrary internal composition (inhomogeneous objects, more different materials, etc.). We exploit orthonormality of spherical harmonics to extract the multipolar moments from a numerical simulation of the polarized object. This can be done in advance (offline) for a set of external electric fields forming a basis so that the superposition principle can then be used for online operation. DEP force and torque can thus be computed in fractions of a second, which is needed, for example, in model-based control applications. We validate the proposed model against reference numerical solutions obtained using Maxwell stress tensor. We also analyze the importance of the higher-order multipolar moments using a sample case of a Tetris-shaped micro-object placed inside a quadrupolar microelectrode array and exposed to electrorotation. The implementation of the model in Matlab and Comsol is offered for free download.