The microwave and submillimeter-wave rotation-tunneling spectra of several mixed deuterated-protonated isotopomers of the water dimer have been measured up to 460 GHz using an electric-resonance optothermal spectrometer, a pulsed-nozzle Fourier-transform microwave spectrometer, and a far-infrared CO2-laser difference-frequency spectrometer. Spectra were recorded for the α-type Kα = 0-0 and 1-1 and b-and/or c-type Kα = 1-0 bands for H2O - DOD, D2O - HOH, D2O - DOH, H2O-HOD, D2O-HOD, H2O - DOH, DHO - HOH, and DHO - DOD, where O - D or O - H denotes the two atoms directly involved in the hydrogen bonding. Spectra of D2O - HOH, H2O - HOD, D2O -HOD, and HDO - HOH, which are higher-energy isomers of H2O - DOD, H2O - DOH, D2O-DOH, and H2O - DOH, respectively, have not been reported previously. These higher-energy isomers are not significantly populated in Ar molecular beams, such as used in many of the previous microwave studies. Here, we obtain information on two of the three major tunneling processes found in the water dimer, the tunneling interchange of the two protons/deuterons on the proton-acceptor subunit and the tunneling interchange of the two protons/deuterons on the proton-donor subunit. The observed rotation-tunneling selection rules are consistent with previously proposed pathways for these tunneling processes. For H2O - DOD, D2O - HOH, and DHO - HOH we find donor interchange tunneling splittings of 24.4(11), 864.14(29), and 1809.39(9) MHz, respectively, averaged over Kα = 0 and 1, and for DHO-DOD we find a donor-interchange tunneling splitting of 16.8(1) MHz for Kα = 0. For DHO - DOD we also determined the proton/deuteron acceptor interchange tunneling splitting for Kα = 0 as 107 723.7(1) MHz, similar to the 117 441.0(2) MHz valued determined previously for DHO - HOD. Because the position of the D/H involved in the hydrogen bonding is nearly coincident with the center of mass of the dimer, isotopomers which only differ by isotopic nuclei at this position have strikingly similar spectra. The present measurements furnish rotational constant and tunneling splitting data to use in the testing and refinement of proposed intermolecular potentials describing water dimer.