We report results from searches for neutral Higgs bosons produced in p-pbar collisions recorded by the Dzero experiment at the Fermilab Tevatron Collider. We study the production of inclusive neutral Higgs boson in the tautau final state and in association with a b quark in the btautau and bbb final states. These results are combined to improve the sensitivity to the production of neutral Higgs bosons in the context of the minimal supersymmetric standard model (MSSM). The data are found to be consistent with expectation from background processes. Upper limits on MSSM Higgs boson production are set for Higgs boson masses ranging from 90 to 300 GeV. We exclude tanBeta>20-30 for Higgs boson masses below 180 GeV. These are the most stringent constraints on MSSM Higgs boson production in p-pbar collisions.