This article presents the results of two studies of Higgs boson properties using the $WW^*(\rightarrow e\nu \mu \nu )jj$ final state, based on a dataset corresponding to ${36.1}{{\mathrm{fb}}^{-1}}$ of $\sqrt{s}=13$ TeV proton–proton collisions recorded by the ATLAS experiment at the Large Hadron Collider. The first study targets Higgs boson production via gluon–gluon fusion and constrains the CP properties of the effective Higgs–gluon interaction. Using angular distributions and the overall rate, a value of $\tan (\alpha ) = 0.0 \pm 0.4 (\mathrm {stat.}) \pm 0.3 (\mathrm {syst.})$ is obtained for the tangent of the mixing angle for CP-even and CP-odd contributions. The second study exploits the vector-boson fusion production mechanism to probe the Higgs boson couplings to longitudinally and transversely polarised W and Z bosons in both the production and the decay of the Higgs boson; these couplings have not been directly constrained previously. The polarisation-dependent coupling-strength scale factors are defined as the ratios of the measured polarisation-dependent coupling strengths to those predicted by the Standard Model, and are determined using rate and kinematic information to be $a_\mathrm {L}=0.91^{+0.10}_{-0.18}$(stat.)$^{+0.09}_{-0.17}$(syst.) and $a_{\mathrm {T}}=1.2 \pm 0.4 $(stat.)$ ^{+0.2}_{-0.3} $(syst.). These coupling strengths are translated into pseudo-observables, resulting in $\kappa _{VV}= 0.91^{+0.10}_{-0.18}$(stat.)$^{+0.09}_{-0.17}$(syst.) and $\epsilon _{VV} =0.13^{+0.28}_{-0.20}$ (stat.)$^{+0.08}_{-0.10}$(syst.). All results are consistent with the Standard Model predictions.