We present a comprehensive study of corrections to electroweak (EW) observables arising from general $SU(2)_L$ scalar multiplets, systematically exploring their impact at both tree and one-loop levels. We first analyze the effects of real scalar multiplet vacuum expectation values (VEVs) on the masses of the $W$ and $Z$ bosons. Then we give the one-loop contributions to the EW oblique parameters $S$, $T$, and $U$ from complex scalar multiplets with arbitrary isospin and hypercharge, in the absence of VEVs. With these general results, we apply this framework to interpret the $W$-boson mass anomaly reported by the CDF-II collaboration. We show that tree-level corrections from VEVs of real multiplets of odd-dimensional representations and vanishing hypercharge can accommodate the observed mass shift while leaving the $Z$-boson mass unaffected. Meanwhile, at the loop level, the inspection of several specific examples shows that complex scalar multiplets could generate sizable contributions to $T$ and $S$, enabling a successful explanation of this $W$-boson anomaly. Particular attention is given to the theoretical bounds on quartic scalar couplings, which provide meaningful constraints on the loop-level solutions.