  Uniaxial strain experiments have become a powerful tool to unveil the
character of unconventional phases of electronic matter. Here we propose a
combination of the superconducting fitness analysis and density functional
theory (DFT) calculations in order to dissect the effects of strain in complex
multi-orbital quantum materials from a microscopic perspective. We apply this
framework to the superconducting state of Sr$_2$RuO$_4$, and argue that the
recently proposed orbitally anti-symmetric spin-triplet (OAST) order parameter
candidate has unique signatures under strain which are in agreement with recent
observations. In particular, we can account for the asymmetric splitting of the
critical temperatures for compressive strain along the $\langle 100\rangle$
direction, and the reduction of the critical temperatures for compressive
strain along the $\langle 001\rangle$ and $\langle 110\rangle$ directions with
a single free parameter.
