The Nd150(He3,t) reaction at 140 MeV/u and Sm150(t,He3) reaction at 115 MeV/u were measured, populating excited states in Pm150. The transitions studied populate intermediate states of importance for the (neutrinoless) ββ decay of Nd150 to Sm150. Monopole and dipole contributions to the measured excitation-energy spectra were extracted by using multipole decomposition analyses. The experimental results were compared with theoretical calculations obtained within the framework of the quasiparticle random-phase approximation, which is one of the main methods employed for estimating the half-life of the neutrinoless ββ decay (0νββ) of Nd150. The present results thus provide useful information on the neutrino responses for evaluating the 0νββ and 2νββ matrix elements. The 2νββ matrix element calculated from the Gamow-Teller transitions through the lowest 1+ state in the intermediate nucleus is maximally about half that deduced from the half-life measured in 2νββ direct counting experiments, and at least several transitions through 1+ intermediate states in Pm150 are required to explain the 2νββ half-life. Because Gamow-Teller transitions in the Sm150(t,He3) experiment are strongly Pauli blocked, the extraction of Gamow-Teller strengths was complicated by the excitation of the 2 ω, ΔL=0, ΔS=1 isovector spin-flip giant monopole resonance (IVSGMR). However, the near absence of Gamow-Teller transition strength made it possible to cleanly identify this resonance, and the strength observed is consistent with the full exhaustion of the non-energy-weighted sum rule for the IVSGMR.