The off equilibrium fluctuation dissipation relations (FDR) are derived to arbitrary order, within the framework of Markovian stochastic evolution, for Ising spins and for continous variables. It is shown that in both cases the FDR do have the same structure. With knowledge of the FDR, zero field algorithms for the efficient numerical computation of the response functions are developed. Two applications are given. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the one dimensional Edwards-Anderson spin glass. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, through the second order FDR, in the case of coarsening systems an effective temperature can be introduced consistently with the one obtained to linear order.