We measured the microwave surface impedances and obtained the superfluid density and flux flow resistivity in single crystals of a phosphor-doped iron-based superconductor SrFe$_2$(As$_{1-x}$P$_{x}$)$_2$ single crystals ($x=0.30$, $T_c=25 mathrm{K}$). At low temperatures, the superfluid density, $n_s (T)/n_s(0)$, obeys a power law, $n_s (T)/n_s (0)=1-C(T/T_c)^n$, with a fractional exponent of $n=1.5$-1.6. The flux flow resistivity was significantly enhanced at low magnetic fields. These features are consistent with the presences of both a gap with line nodes and nodeless gaps with a deep minimum. The remarkable difference observed in the superconducting gap structure between SrFe$_2$(As$_{1-x}$P$_{x}$)$_2$ and BaFe$_2$(As$_{1-x}$P$_{x}$)$_2$ in our experiments is important for clarifying the mechanism of iron-based superconductivity.