We consider the task-oriented modeling of the differential kinematics of nonholonomic mobile manipulators (NMMs). A suitable NMM Jacobian is defined that relates the available input commands to the time derivative of the task variables, and can be used to formulate and solve kinematic control problems. When the NMM is redundant with respect to the given task, we provide an extension of two well-known redundancy resolution methods for fixed-base manipulators (Projected Gradient and Task Priority) and introduce a novel technique (Task Sequencing) aimed at improving performance, e.g., avoiding singularities. The proposed methods are applied then to the specific case of image-based visual servoing, where the NMM image Jacobian combines the interaction matrix and the kinematic model of the mobile manipulator. Comparative numerical results are presented for two case studies.