  In this work we calculate the mass spectrum of strangeonium up to the $3D$
multiplet within a nonrelativistic linear potential quark model. Furthermore,
using the obtained wave functions, we also evaluate the strong decays of the
strangeonium states with the $^3P_0$ model. Based on our successful
explanations of the well established states $\phi(1020)$, $\phi(1680)$,
$h_1(1415)$, $f'_2(1525)$, and $\phi_3(1850)$, we further discuss the possible
assignments of strangeonium-like states from experiments by combining our
theoretical results with the observations. It is found that some resonances,
such as $f_2(2010)$ and $f_2(2150)$ listed by the Particle Data Group, and
$X(2062)$ and $X(2500)$ newly observed by BESIII, may be interpreted as the
strangeonium states. The possibility of $\phi(2170)$ as a candidate for
$\phi(3S)$ or $\phi(2D)$ cannot be excluded. We expect our results to provide
useful references for looking for the missing $s\bar{s}$ states in future
experiments.
