  Oscillation modes of compact stars, in general, can serve as a fingerprint in
determining the equation of state (EOS) of dense matter. In this study, we
examine the impact of symmetry energy slope ($L$) on the oscillation
frequencies of neutron stars (NSs) with nucleon-nucleon short range correlation
(SRC) and admixed dark matter (DM) for the first time within the relativistic
mean-field theory. By adjusting the $L$, we revise the EOS and coupling
parameters in light of the SRC and DM effects, and construct the new sets. The
results reveal that NSs containing SRC and DM inside are more likely to satisfy
the observational constraints, and we find that smaller $L$ exhibits larger
fundamental non-radial and radial frequencies, and that the effect on Large
Separation (LG) is also mainly concentrated in the low-mass region. Moreover,
we update the linear relationship between the non-radial frequency and mean
density, and we further give empirical relations between non-radial and radial
frequencies and tidal deformability at different $L$ for 1.4$M_{\odot}$ and
2$M_{\odot}$. These findings will enable us to more effectively confine the NS
EOSs, in turn, also provide a strategy to place constraints on the $L$.
