Most conceptual designs for future laser wakefield accelerators (LWFA) require external injection of precisely-phased, monoenergetic, ultrashort bunches of MeV electrons. This paper reports simulation and Hamiltonian models of several nonideal injection schemes that demonstrate strong phase bunching and good accelerated beam quality in a channel-guided LWFA. For the case of monoenergetic, unphased (long bunch) injection, there is an optimum range of injection energies for which the LWFA can trap a significant fraction of the injected pulse while producing an ultrashort, high-quality accelerated pulse. These favorable results are due to a combination of pruning of particles at unfavorable phases, rapid acceleration, and strong phase bunching. Also, the plasma channel introduces a favorable shift in the region of accelerating phase where electrons are focused, which can significantly reduce the required injection energy. Simulation results agree well with the predictions of the Hamiltonian model. Simulations of phased injection with a broad injected energy spread also exhibit final accelerated bunches with small energy spread. These results suggest that relatively poor quality injection pulses may still be useful in LWFA demonstration experiments.