In this article, the output consensus problems of nonlinear strict-feedback multi-agent systems with both external disturbance and sensor uncertainties are studied. To begin with, the original system is shifted to a strict-feedback system by a state transformation, where all the unknown information is lumped into the last state equation. Specially, the outputs of the transformed system and the original system are identical. Then, for the transformed system, an observer is constructed to get the estimated state. For the sake of the disturbance rejection, a distributed unknown input reconstructing scheme is put forward via an interval observer which decouples the control input. Further, for the transformed system, a distributed controller is erected by introducing state estimates and reconstructed unknown inputs to realize output consensus. Eventually, two simulation examples are designed to verify the performance and comparison result of the proposed method.