Delayed impulsive controllers are proposed in this paper to enable the agents in a class of second-order multiagent systems (MASs) to achieve state consensus, based, respectively, on the relative full-state and partial-state sampled-data measurements among neighboring agents. It is a challenging task to analyze the consensus behaviors of the considered MASs as the dynamics of such MASs will be subjected to joint effects from delay-dependent impulses, aperiodic sampling, and switchings among different communication graphs. A novel analytical approach, based upon the discretization method, state augmentation, and linear state transformation, is developed to establish the sufficient consensus criteria on the range of the impulsive intervals and the control parameters. Remarkably, it is found that consensus in the closed-loop MASs can be always ensured by skillfully selecting the control parameters as long as the nonuniform delays and the impulsive intervals are bounded. A numerical example is finally performed to validate the effectiveness of the proposed delayed impulsive controllers.