  The lasting puzzle of the superconducting order parameter of Sr$_2$RuO$_4$
calls for theoretical studies that include seldom-considered effects. Here we
include spin-orbit coupling effects on the electronic structure and then solve
the linearized Eliashberg equation in a pseudospin basis, including the
possibility that spin and charge fluctuations induce frequency-dependent
superconducting order parameters. We find that spin-orbit coupling mixes even
and odd contributions in orbital, spin and frequency spaces and that leading
inter-pseudospin symmetries, B$_{1g}^+$ and A$_{2g}^-$, have intra-orbital
components respectively even and odd in Matsubara frequency. An accidental
degeneracy between these could resolve apparent experimental contradictions.
