The 16O(7Li)19F reaction has been investigated at an incident energy of 20 MeV. Complete angular distributions were measured in the angular range lab=7.5°-157.5°using a multiangle spectrograph. Known (sd)3 states are populated about twice as strongly as the core-excited four-particle "one-hole (4p-1h) states. Angular distributions for members of the ground-state band show only a moderate forward-angle rise and those of the negative-parity band and other weak states are approximately symmetric around 90°. Results have been analyzed in terms of Hauser-Feshbach compound-nucleus calculations and finite-range distorted-wave Born approximation calculations in which the three transferred nucleons enter the sd and/or 1p shells. The contribution of the compound-nucleus cross section has been estimated. The data for the K=12 and K=12 bands in 19F could be well fitted by an incoherent sum of direct and compound reaction cross sections. Simple analysis of the integrated cross sections based on a (2J+1) rule is consistent with results of the Hauser-Feshbach calculations. Comparison between the present experimental results and previous triton cluster transfer reactions on 16O emphasizes the enhanced compound/direct ratio for the 4p-1h and other weak states in the present data.