We report the results of a study of the exclusive charmless semileptonic decays, B0→π -+ν, B +→π0 +ν, B +→ω +ν, B +→η +ν, and B +→η ′+ν (=e or μ) undertaken with approximately 462×106 BB̄ pairs collected at the Υ(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 q2, the square of the momentum transferred to the lepton-neutrino pair, for B0→π -+ν, B +→π0 +ν, B +→ω +ν, and B +→η +ν. From these distributions, we extract the form-factor shapes f +(q2) and the total branching fractions B(B0→π -+ν)=(1.45±0.04 stat±0.06 syst)×10 -4 (combined π - and π0 decay channels assuming isospin symmetry), B(B +→ω +ν)=(1.19±0.16 stat±0.09 syst)×10 -4 and B(B +→η +ν)=(0.38±0.05 stat±0.05 syst)×10 -4. We also measure B(B +→η ′+ν)=(0.24±0. 08 stat±0.03 syst)×10 -4. We obtain values for the magnitude of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V ub| by direct comparison with three different QCD calculations in restricted q2 ranges of B→π +ν decays. From a simultaneous fit to the experimental data over the full q2 range and the FNAL/MILC lattice QCD predictions, we obtain |V ub|=(3.25±0.31)×10 -3, where the error is the combined experimental and theoretical uncertainty. © 2012 American Physical Society.