  A pivotal challenge posed by unconventional superconductors is to unravel how
superconductivity emerges upon cooling from the generally complex normal state.
Some of the most prominent unconventional superconductors are oxides: strontium
titanate, strontium ruthenate, and the cuprates exhibit greatly different
superconducting transition temperatures $T_c$, and although their respective
superconducting pairing mechanisms remain unknown, they are thought to differ
as well. Here we use nonlinear magnetic response, a probe that is uniquely
sensitive to the superconducting precursor, to uncover remarkable universal
behavior in these three distinct classes of superconductors. We find unusual
exponential temperature dependence of the diamagnetic response above the
transition temperature $T_c$, with a characteristic temperature scale that
strongly varies with $T_c$. We correlate this scale with the sensitivity of
$T_c$ to local stress, and show that it is influenced by intentionally-induced
structural disorder. The universal behavior is therefore caused by intrinsic,
self-organized structural inhomogeneity, inherent to the oxides
perovskite-based structure. The prevalence of such inhomogeneity has
far-reaching implications for the interpretation of electronic properties of
perovskite-related oxides in general.
