We present, in detail, a search for the standard model Higgs boson, H, in final states with a charged lepton (electron or muon), missing energy, and two or more jets in data corresponding to 9.7 fb−1 of integrated luminosity collected at a center of mass energy of s = 1.96 TeV with the D0 detector at the Fermilab Tevatron ppˉ Collider. The search uses b-jet identification to categorize events for improved signal versus background separation and is sensitive to associated production of the H with a W boson, WH→ℓνbbˉ; gluon fusion with the Higgs decaying to W boson pairs, H→WW→ℓνjj; and associated production with a vector boson where the Higgs decays to W boson pairs, VH→VWW→ℓνjjjj production (where V=W or Z). We observe good agreement between data and expected background. We test our method by measuring WZ and ZZ production with Z→bbˉ and find production rates consistent with the standard model prediction. For a Higgs boson mass of 125 GeV, we set a 95%\ C.L. upper limit on the production of a standard model Higgs boson of \obslimA×σSM, where σSM is the standard model Higgs boson production cross section, while the expected limit is \explimA×σSM. We also interpret the data considering models with fourth generation fermions, or a fermiophobic Higgs boson