Five mutually exclusive searches for supersymmetry are presented based on events in which b jets and four W bosons are produced in proton-proton collisions at sqrt(s) = 8 TeV. The data, corresponding to an integrated luminosity of 19.5 inverse femtobarns, were collected with the CMS experiment at the CERN LHC in 2012. The five studies differ in the leptonic signature from the W boson decays, and correspond to all-hadronic, single-lepton, opposite-sign dilepton, same-sign dilepton, and greater-than-or-equal-to-3 lepton final states. The results of the five studies are combined to yield 95% confidence level limits for the gluino and bottom-squark masses in the context of gluino and bottom-squark pair production, respectively. In the limit when the lightest supersymmetric particle is light, gluino and bottom-squark masses are excluded below 1280 and 570 GeV, respectively.