Two analyses are performed with the large samples of dielectron and dimuon events collected by the D0 experiment at the Fermilab Tevatron $p\bar{p}$ collider. The dilepton transverse momentum ($p_T$) distribution in $Z/\gamma^* → \ell^+\ell^-$ production is a powerful probe of Quantum chromodynamics. Until now, this distribution has been measured with limited precision. An alternative variable, $\phi^*_\eta$, is proposed due to its relatively low susceptibility to detector effects. The $\phi^*_\eta$, distribution of events with $Z/\gamma^* → \ell^+\ell^-$ invariant masses between 70 and 110 GeV, is measured in three bins of dilepton rapidity. This measurement, with 7.3 fb$^{-1}$ of data, is significantly more precise than previous measurements of the $p_T$ distribution. A state-of-the-art QCD Monte Carlo program is in modest agreement with the data. Using 8.6 fb$^{-1}$ of data, the $ZZ/\gamma^* → \nu\bar{\nu}\ell^+\ell^-$ and $WZ/\gamma^* → \ell\nu\ell^+\ell^-$ processes are studied, yielding production cross sections of, $\sigma(p\bar{p} \rightarrow ZZ/\gamma^*)$ = 1.64 $\pm$ 0.46 p b and $\sigma(p\bar{p} \rightarrow WZ/\gamma^*)$ = 4.46 $\pm$ 0.64 pb, for $Z/\gamma^* → \ell^+\ell^-$ invariant masses between 60 and 130 GeV. These are in agreement with Standard Model predictions.