Searches for new heavy resonances decaying into different pairings of $W$, $Z$, or Higgs bosons, as well as directly into leptons, are presented using a data sample corresponding to $36.1{\mathrm{fb}}^{-1}$ of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ collected during 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting bosonic decay modes in the $qqqq$, $\nu \nu qq$, $\ell \nu qq$, $\ell \ell qq$, $\ell \nu \ell \nu$, $\ell \ell \nu \nu$, $\ell \nu \ell \ell$, $\ell \ell \ell \ell$, $qqbb$, $\nu \nu bb$, $\ell \nu bb$, and $\ell \ell bb$ final states are combined, searching for a narrow-width resonance. Likewise, analyses selecting the leptonic $\ell \nu$ and $\ell \ell$ final states are also combined. These two sets of analyses are then further combined. No significant deviation from the Standard Model predictions is observed. Three benchmark models are tested: a model predicting the existence of a new heavy scalar singlet, a simplified model predicting a heavy vector-boson triplet, and a bulk Randall-Sundrum model with a heavy spin-2 Kaluza-Klein excitation of the graviton. Cross section limits are set at the 95% confidence level using an asymptotic approximation and are compared with predictions for the benchmark models. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The data exclude a heavy vector-boson triplet with mass below 5.5 TeV in a weakly coupled scenario and 4.5 TeV in a strongly coupled scenario, as well as a Kaluza-Klein graviton with mass below 2.3 TeV.