  We study the pairing symmetry of Sr$_2$RuO$_4$ through the group-theoretical
approach. We emphasize the role of pairing interaction between the
quasi-one-dimensional(Q1D) $d_{xz/yz}$ and quasi-two-dimensional(Q2D) $d_{xy}$
orbitals. It is found that two degenerate inter-orbital
time-reversal-invariant(TRI) p-wave pairings, one is spin-singlet and the other
spin-triplet with out-of-plane $\bm{d}$-vector, could be the most promising
candidates. Several important physical quantities are presented, including the
near-nodal gap structure, the unchanged out-of-plane Knight shift, and no split
transition under strain, which are consistent with the experiments. In
addition, these p-wave pairings shed light on resolving the contradiction
between the time-reversal breaking and reduced in-plane Knight shift
measurements. As the system reaches the Van Hove singularity under applied
strain, the pairing symmetry would become a d-wave pairing mainly consisting of
inter-orbital components, which could be responsible for the strained 3$K$
phase.
