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 À1 of integrated luminosity collected at a center-of-mass energy of ffiffi ffi s p ¼ 1:96 TeV with the D0 detector at the Fermilab Tevatron p " p 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,b; gluon fusion with the Higgs decaying to W-boson pairs, H ! WW ! ' jj; and associated production with a vector boson where the Higgs decays to W-boson pairs, VH ! VWW ! ' jjjj production (where V ¼ W or Z). We observe good agreement between data and expected background. We test our method by measuring WZ and ZZ production with Z ! b " b 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 5:8 Â SM , where SM is the standard model Higgs boson production cross section, while the expected limit is 4:7 Â SM . We also interpret the data considering models with fourth generation fermions, or a fermiophobic Higgs boson.