You've got `Evaluate` in the wrong place.  It has to be of the form

    Plot[Evaluate[stuff to plot...],...]

So this seems to work:

    Manipulate[
     Plot[Evaluate@{
       (ReplaceAll[Paorta[t], 
          NDSolve[{Paorta'[t] == 
             1/Caorta ((1/2*k*(1 + Cos[ω t]) + 10 - Paorta[t])/
                 Piecewise[{{Ro, 
                    1/2*k*(1 + Cos[ω t]) + 10 - Paorta[t] > 0}}, 
                  x*Ro] - Paorta[t]/Rsystemic), 
            Paorta[0] == 90}, {Paorta[t]}, {t, 0, 10}]]),
        (1/2*k*(1 + Cos[ω t]) + 10),
        (((1/2*k*(1 + Cos[ω t]) + 10) - 
            ReplaceAll[Pao[t], 
             NDSolve[{Pao'[t] == 
                1/Caorta ((1/2*k*(1 + Cos[ω t]) + 10 - Pao[t])/
                    Piecewise[{{Ro, 1/2*k*(1 + Cos[ω t]) + 10 - Pao[t] > 0}}, 
                     x*Ro] - Pao[t]/Rsystemic), 
               Pao[0] == 90}, {Pao[t]}, {t, 0, 10}]])/Ro)}, {t, 0, 10}, 
      ImageSize -> Large, PlotRange -> Full, 
      PlotLegends -> {"Aortic Pressure", "Pressure in Left Ventricle", "Flow"}],
     {{Caorta, 1/.48}, 1, 6},
     {{Rsystemic, 3.1}, .1, 6},
     {{x, 8000}, 1, 10000},
     {{ω, 2 π}, π, 3 π},
     {{k, 110}, 60, 200},
     {{Ro, .01}, .007, .05}]

`Plot` has the attribute [`HoldAll`](http://reference.wolfram.com/language/ref/HoldAll.html).  [`Evaluate`](http://reference.wolfram.com/language/ref/Evaluate.html) overrides holding an argument exactly when it is the `Head` of the argument.  That's why the placement is important.

----

Re: Additional request for simplification.

Put the `ReplaceAll` (`/.`) outside the list of things to plot.  It will, after all, *replace all* instances of `Paorta`. :)

    Manipulate[Plot[
      Evaluate[
       {Paorta[t],
        (1/2*k*(1 + Cos[ω t]) + 10),
        (((1/2*k*(1 + Cos[ω t]) + 10) - Paorta[t])/Ro)
       } /. NDSolve[{Paorta'[t] == 
           1/Caorta ((1/2*k*(1 + Cos[ω t]) + 10 - Paorta[t])/
               Piecewise[{{Ro, 1/2*k*(1 + Cos[ω t]) + 10 - Paorta[t] > 0}}, 
                x*Ro] - Paorta[t]/Rsystemic), 
          Paorta[0] == 90}, {Paorta[t]}, {t, 0, 10}]
       ],
      {t, 0, 10}, ImageSize -> Large, PlotRange -> Full, 
      PlotLegends -> {"Aortic Pressure", "Pressure in Left Ventricle", "Flow"}],
     {{Caorta, 1/.48}, 1, 6},
     {{Rsystemic, 3.1}, .1, 6},
     {{x, 8000}, 1, 10000},
     {{ω, 2 π}, π, 3 π},
     {{k, 110}, 60, 200},
     {{Ro, .01}, .007, .05}]