The crystal structure of BiMnO3+δ ceramics has been studied as a function of nominal oxygen excess and temperature using synchrotron and neutron powder diffraction, magnetometry and differential scanning calorimetry. Increase in oxygen excess leads to the structural transformations from the monoclinic structure (C2/c) to another monoclinic (P21/c), and then to the orthorhombic (Pnma) structure through the two-phase regions. The sequence of the structural transformations is accompanied by a modification of the orbital ordering followed by its disruption. Modification of the orbital order leads to a rearrangement of the magnetic structure of the compounds from the long-range ferromagnetic to a mixed magnetic state with antiferromagnetic clusters coexistent in a ferromagnetic matrix followed by a frustration of the long-range magnetic order. Temperature increase causes the structural transition to the nonpolar orthorhombic phase regardless of the structural state at room temperature; the orbital order is destroyed in compounds BiMnO3+δ (δ ≤ 0.14) at temperatures above 470 °C.