We report the first measurements of a complete second-order cumulant matrix of net-charge, net-proton, and net-kaon multiplicity distributions for the first phase of the beam energy scan program at the Relativistic Heavy Ion Collider. This includes the centrality and, for the first time, the pseudorapidity window dependence of both diagonal and off-diagonal cumulants in Au+Au collisions at sNN= 7.7-200 GeV. Within the available acceptance of |η|<0.5, the cumulants grow linearly with the pseudorapidity window. Relative to the corresponding measurements in peripheral collisions, the ratio of off-diagonal over diagonal cumulants in central collisions indicates an excess correlation between net-charge and net-kaon, as well as between net-charge and net-proton. The strength of such excess correlation increases with the collision energy. The correlation between net-proton and net-kaon multiplicity distributions is observed to be negative at sNN= 200 GeV and change to positive at the lowest collision energy. Model calculations based on nonthermal (UrQMD) and thermal (HRG) production of hadrons cannot explain the data. These measurements will help map the quantum chromodynamics phase diagram, constrain hadron resonance gas model calculations and provide new insights on the energy dependence of baryon-strangeness correlations.