The spectroscopic parameters and decay channels of the doubly charged scalar, pseudoscalar and axial-vector charm–strange tetraquarks Z_{ overline{c}s}=[sd][overline{u} overline{c}] are explored within framework of the QCD sum rule method. The masses and current couplings of these diquark–antidiquark states are calculated by means of two-point correlation functions and taking into account the vacuum condensates up to eight dimensions. To compute the strong couplings of Z_{overline{c}s} states with D, D_{s}, D^{*}, D_{s}^{*}, D_{s1}(2460), D_{s0}^{*}(2317), pi and K mesons we use QCD light-cone sum rules and evaluate width of their S- and P-wave decays to a pair of negatively charged conventional mesons: For the scalar state Z_{overline{c}s}rightarrow D_s pi , DK, D_{s1}(2460)pi , for the pseudoscalar state Z_{overline{c}s} rightarrow D_{s}^{*}pi , D^{*}K, D_{s0}^{*}(2317)pi , and for the axial-vector state Z_{overline{c}s} rightarrow D_{s}^{*}pi , D^{*}K, D_{s1}(2460)pi decays are investigated. Obtained predictions for the spectroscopic parameters and decay widths of the Z_{overline{c}s} tetraquarks may be useful for experimental investigations of the doubly charged exotic hadrons.