The recovery algorithms of the finite impulse responses (FIRs) of multipath channels via a single-measurement-vector and a multiple-measurement-vector, respectively, are investigated in the massive multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Based on the characteristics of the spatial-temporal block sparse structure of the multipath channels, the phase-shift orthogonal comb pilots are designed and inserted into the symbols to ensure the column uncorrelatedness of the sensing matrix. These pilot tones are spread among all transmit antennas. For the purpose of resolving the difficulty of approximating the unknown sparsity without overestimation, the robust sparsity adaptive matching pursuit (RSAMP) algorithms to be used in both measurement scenarios are proposed. The residuals in these algorithms are smoothened within several iterations but achieving much more acceptable halting state. The proposed algorithms are proven to be immune to the size of the support set and a flexible number of measurement vectors. Simulations demonstrate that the normalized mean square error performance of these algorithms is comparable to those of the orthogonal matching pursuit algorithm and the subspace pursuit algorithm.