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The stellar death and its aftermath are compelling systems to study due to their extreme conditions and a rich array of observable messengers, such as photons, gravitational waves, and neutrinos. Neutrinos, as messengers of these systems, are particularly interesting due to their ability to traverse space unimpeded by interstellar debris, magnetic fields, or photons, thus preserving important information about the source, with different sites of production that influence the neutrino energy from nuclear processes in very dense and hot environments producing thermal MeV energy neutrinos to cosmic acceleration sites, where matter collides in shocks, producing high energy neutrinos in the O(>GeV-TeV). These neutrinos can be observed by neutrino telescopes such as the IceCube Neutrino Observatory, which has sensitivity for neutrinos from the MeV to >PeV energy ranges. In this thesis, we performed several searches, focusing on MeV neutrinos from Gamma Ray Bursts and Neutron Star Mergers, making use of information from other messengers such as photons and gravitational waves to inform our search, and >GeV neutrinos from Core-Collapse Supernovae. We produced MeV neutrino flux limits for GRB 221009A and provided detection horizon limits for >GeV neutrinos from Core-Collapse Supernovae. We also introduced a novel methodology for producing model-independent MeV neutrino flux and luminosity limits, developed a new IceCube MeV energy real-time fast analysis for the follow-up of external alerts from other observatories, and demonstrated how to search for MeV neutrinos correlated with gravitational waves.