We study theoretically the electronic structures of various group III acceptors in Ge under  stress, based on the effective-mass theory with a semi-empirical impurity potential which considers the q-dependent screening and the central-cell correction. An assignment is made for inter-level transition lines which were previously ignored or incorrectly assigned. In addition, our calculation can resolve crowding levels of final states of transition lines which have not been resolved by experimental techniques. The stress effect on the electronic structure can be understood by connecting with the composition of the states. Our results show that the binding energies decrease rapidly with the stress in the low-stress region, and for even-parity states they exhibit remarkable asymmetry in the stress dependence due to the large difference between the heavy-hole and the light-hole compositions. The acceptor states asymptotically approach a pure heavy-hole or light-hole state under high stress. In the limiting case of high stress, extra degeneracy appears. The central-cell correction may cause a significant chemical shift for even-parity states of nonisocoric acceptors. We also complete the assignment of the four line components into which the B line splits under stress. The newly assigned stress-dependent transition energies show excellent agreement with the experimental data for low stress. A justification is made for the applicability of our calculation scheme to the case of high stress.