The results of the first experimental studies on the structural (lattice parameters) and elastic characteristics of ErBaCo4O7 + x cobaltites in the range of structural and magnetic phase transitions are presented. The samples obtained using different thermal treatments and characterized by a small oxygen excess x are studied. It is found that the parameter Δa/a for the stoichiometric ErBaCo4O7 sample annealed in vacuum exhibits no anomalies in the course of a structural transition, whereas the parameters b and c undergo stepwise changes of opposite signs. The different values of these changes Δb/b ≈ 4 × 10−3 and Δc/c ≈ −5 × 10−3 result in the stepwise volume change ΔV/V ≈ −10−3. A slight deviation from the oxygen stoichiometry affects the character of the structural distortion; namely, the magnitude of the anisotropic strain and the sign of the isotropic strain change. The structural distortion in the stoichiometric sample is accompanied by a sharp stepwise change in the Young’s modulus ΔE(T)/E0 ∼ 8 × 10−2, whereas the magnitude of elastic anomalies near TS in slightly nonstoichiometric samples with x ∼ 0.03 decreases by an order of magnitude. Comparison of elastic anomalies manifesting themselves near the magnetic phase transition temperature TN for distorted samples with different deviations from stoichiometry suggests that the arising long-range magnetic order in the cobalt subsystem is apparently affected not only by structural distortions but also by disorder introduced by nonstoichiometric oxygen.