In a superconductor with finite spin-orbit coupling (SOC), neither the orbital nor the spin angular momentum of a Cooper pair is good quantum number, but their sum is. We focus on two aspects of the SOC-influenced superconductivity in Sr₂RuO₄. In the first[1,2], we argue that the most frequently discussed p-wave state in the E_u representation, which has Cooper pair angular momentum |L_z,S_z〉= |±1,0〉, must coexist with another pairing with |L_z,S_z〉=|0,±1〉. The two correspond respectively to the gap functions (k_x,k_y)\hat{z} and k_z(\hat{x},\hat{y}) in the d-vector notation. If the latter dominates, the E_u superconducting channel would favor a nematic rather than a chiral state. Moreover, in-plane uniaxial strains, which primarily perturb the orbital angular momentum L_z of the Cooper pairs, split the components in the |±1,0〉pairing linearly and those in the |0,±1〉 pairing quadratically. In the second[3], we show how SOC may inherently entangle spin-triplet and spin-singlet pairings in multi-orbital models of Sr₂RuO₄. Possible relevance to the recent experiments, such as the uniaxial strain and NMR Knight shift measurements, will be discussed. Refs: [1] Huang and Yao, PRL 121, 157002 (2018); [2] Huang, Zhou, and Yao, arXiv:1901.07041; [3] Huang, Zhou, and Yao, PRB 100, 134506 (2019).