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 $sbar{s}$ states in future experiments.
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