We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollinear magnetic states, thus providing evidence for generation of spin-triplet superconductivity. A quantitative analysis brings us to a conclusion that the triplet current in out Ni-based spin-valves is approximately three times larger than the conventional singlet supercurrent.