The equilibrium structure, electronic properties and potential energy surfaces of interstitial oxygen (Oi) in c-C, Si, BP, AlP, c-SiC and c-BN are calculated in small and large molecular clusters. The theoretical level ranges from the 'approximate ab initio' Hartree-Fock method of partial retention of diatomic differential overlap to large-basis-set ab initio Hartree-Fock followed by second-order corrections for electron correlation (MP2). The equilibrium site is a puckered bridged bond in all hosts. In compound semiconductors, Oi has a larger degree of bonding with the most electronegative of the two host atoms (P, C or N) than with the least electronegative one and puckers in a direction that maximizes the overlap with its second-nearest neighbour. The dipole moment of the defect and the barrier for reorientation of Oi around and through the (111) axis are calculated. In order to estimate the relative stability of Oi in the various hosts, we determine the energies involved in inserting molecular O2 into the lattice and dissociating it into two isolated Ois. Finally, we calculate the barriers for migration of Oi between adjacent equilibrium sites. There are two such barriers in compound semiconductors. Whenever possible, we correlate the properties of Oi with various properties of the host, such as its and length and its ionic character, in order to gain predictive insight into the fundamental properties of interstitial oxygen in semiconductors.