The reaction 8 Li + 2 H has been studied in inverse kinematics at the incident energy of 3.15 MeV/nucleon, using the REX-ISOLDE post-accelerator. The reaction channels corresponding to (d, p), (d, d), and (d, t) reactions populating ground states and low-lying excited states in [7][8][9] Li have been identified and the related angular distributions extracted and compared with coupled-channels, distorted-wave Born approximation (DWBA), and coupled-reaction-channels calculations. For the inelastic and (d, t) channels we find that higher order effects are very important and hence one needs to go beyond the simple DWBA to extract reliable structure information from these processes.