Despite the success of discovering transiting exoplanets, several recently observed objects (e.g. KIC-8462852, J1407 and PDS-110) exhibit unconventional transit signals, whose appropriate interpretation in terms of a spherical single body has been challenging, if not impossible. In the aforementioned examples the presence of a ring-like structure has been proposed for explaining the unusual data. Thus, in this paper we delve into the dynamics of a tilted exoring disturbed by a third close companion, and the role that the Lidov-Kozai mechanism may have to explain irregular and anomalous transit signals of ringed planets, as well as the ring's early stages. To that end, we performed numerical simulations and semi-analytical calculations to assess the ring's dynamical and morphological properties, and their related transit observables. We found that tilted ringed structures undergo short-term changes in shape and orientation that are manifested as strong variations of transit depth and contact times, even between consecutive eclipses. Any detected anomaly in transit characteristics may lead to a miscalculation of the system's properties (planetary radius, semi-major axis, stellar density and others). Moreover, oscillating ring-like structures may account for the strangeness of some light-curve features in already known and future discovered exoplanets.