Abstract: We report the results of a study of the exclusive charmless semileptonic decays, B-0 -> pi(-)l(+)nu, B+ -> pi(0)l(+)nu, B+ -> omega l(+)nu, B+ -> eta l(+)nu, and B+ -> eta'l(+)nu (l = e or mu) undertaken with approximately 462 X 10(6) B (B) over bar pairs collected at the Upsilon(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with a loose neutrino reconstruction technique. We obtain partial branching fractions in several bins of q(2), the square of the momentum transferred to the lepton-neutrino pair, for B-0 -> pi(-)l(+)nu, B+ -> pi(0)l(+)nu, B+ -> omega l(+)nu, and B+ -> eta l(+)nu. From these distributions, we extract the form-factor shapes f(+)(q(2)) and the total branching fractions B(B-0 -> pi(-)l(+)nu) = (1.45 +/- 0.04(stat) +/- 0.06(syst)) X 10(-4) (combined pi(-) and pi(0) decay channels assuming isospin symmetry), B(B+ -> omega l(+)nu) = (1.19 +/- 016(stat) +/- 0.09(syst)) X 10(-4) and B(B+ -> eta l(+)nu) = (0.38 +/- 0.05(stat) +/- 0.05(syst)) X 10(-4). We also measure B(B+ -> eta'l(+)nu) = (0.24 +/- 0.08(stat) +/- 0.03(syst)) X 10(-4). We obtain values for the magnitude of the Cabibbo-Kobayashi-Maskawa (KM) matrix element vertical bar V-ub vertical bar by direct comparison with three different QCD calculations in restricted q(2) ranges of B -> pi l(+)nu decays. From a simultaneous fit to the experimental data over the full q(2) range and the FNAL/MILC lattice QCD predictions, we obtain vertical bar V-ub vertical bar = (3.25 +/- 0.31) X 10(-3), where the error is the combined experimental and theoretical uncertainty.