We study the detection prospects of relatively light charged scalars in radiative Majorana neutrino mass models, such as the Zee model and its variants using scalar leptoquarks, at current and future neutrino telescopes. In particular, we show that these scalar mediators can give rise to Glashow-like resonance features in the ultrahigh energy (UHE) neutrino event spectrum at the IceCube neutrino observatory and its high-energy upgrade IceCube-Gen2. The same scalars can also give rise to observable nonstandard neutrino interactions (NSIs), and we show that the UHE neutrinos provide a complementary probe of NSI. We also discuss an interesting possibility of producing such resonances by incoming sterile neutrino components in the case where neutrinos are pseudo-Dirac particles.