Electron-hole hybridization in InAs/GaSb double quantum well structures leads to the formation of a miniband- gap. We experimentally and theoretically studied the impact of strain on the transport properties of this material system. Thinned samples were mounted to piezoelectric elements to exert strain along the [011] and [001] crystal directions. When the Fermi energy is tuned through the minigap, the resistivity at the charge neutrality point is found to be susceptible to external strain. In the electron and hole regimes, strain influences the Landau level structure. By analyzing the intrinsic strain from the epitaxial growth and the external strain from the piezo elements and combining our experimental results with numerical simulations of strained and unstrained quantum wells, we can illustrate why the InAs/GaSb material system is regularly found to be semimetallic.