The current status in Prime 3 is that the ODE line solvers and odesolve will accept units with the variables. As shown in the attached file, the Rkadapt and Bulstorer methods get the correct answer in terms of the default units, but the units are not shown. They should all be consistent, showing the units for the results.
All of the dependent variables must have the same dimension in all but two of the solvers...odesolve and rkfixed. In odesolve and rkfixed, each ODE and dependent variable may have a different dimension. Since odesolve can automatically call RKadapt and other solvers, it is not clear if those solvers operate with multiple dimensions in odesolve. Since we cannot manually select the method in odesolve, there is no way to test.