  We investigate the combined effect of Hund's and spin-orbit (SO) coupling on
superconductivity in multi-orbital systems. Hund's interaction leads to
orbital-singlet spin-triplet superconductivity, where the Cooper pair wave
function is antisymmetric under the exchange of two orbitals. We identify three
d-vectors describing even-parity orbital-singlet spin-triplet pairings among
t2g-orbitals, and find that the three d-vectors are mutually orthogonal to each
other. SO coupling further assists pair formation, pins the orientation of the
d-vector triad, and induces spin-singlet pairings with a relative phase
difference of \pi/2. In the band basis the pseudospin d-vectors are aligned
along the z-axis and correspond to momentum-dependent inter- and intra-band
pairings. We discuss quasiparticle dispersion, magnetic response, collective
modes, and experimental consequences in light of the superconductor Sr2RuO4.
