We investigated the influence of oxygen overstoichiometry on apical oxygen disorder and magnetic correlations in Nd2NiO4+delta (delta similar to 0.11) in the temperature range of 2-300 K by means of synchrotron x-ray powder diffraction, neutron single-crystal and powder diffraction studies, combined with macroscopic magnetic measurements. In the investigated temperature range, the compound crystallizes in a tetragonal commensurate structure with a P4(2)/ncm space group with excess oxygen atoms occupying the 4b (3/4 1/4 1/4) interstitial sites, coordinated by four apical oxygen atoms. Large and anisotropic thermal displacement parameters are found for equatorial and apical oxygen atoms, which are strongly reduced on an absolute scale compared to the Nd2NiO4.23 phase. Maximum entropy analysis of the neutron single-crystal diffraction data uncovered anharmonic contributions to the displacement parameters of the apical oxygen atoms, toward the nearest vacant 4b interstitial site, related to the phonon-assisted oxygen diffusion mechanism. Macroscopic magnetization measurements and neutron powder diffraction studies reveal long-range antiferromagnetic ordering of the Ni sublattice at T-N similar to 53K with a weak ferromagnetic component along the c axis, while the long-range magnetic ordering of the Nd sublattice occurs below 10 K. Temperature-dependent neutron diffraction patterns show the appearance of a commensurate magnetic order at TN with the propagation vector k = (100) and the emergence of an additional incommensurate phase below 30 K, while both phases coexist at 2 K. The commensurate magnetic structure is best described by the P4(2)/nc'm' Shubnikov space group. Refined magnetic moments of the Ni and Nd sites at 2 K are 1.144(76) and 1.632(52) mu(B), respectively. A possible origin of the incommensurate phase is discussed and a tentative magnetic phase diagram is proposed.