The recent observation of CNO solar neutrinos by Borexino (BX) has proven the high potential offered by large underground ultrapure liquid scintillators to disclose weak neutrino and antineutrino fluxes. Supernovae explosions, gamma-ray bursts, solar flares and Gravitational Waves (GW) are among the possible extra-terrestrial sources of neutrinos and antineutrinos. The extreme radiopurity of the BX detector has already allowed to get the best upper limits on all flavor fluences in the few MeV energy range from gamma ray bursts, to set limits on the diffuse supernova antineutrino background in the unexplored energy region below 8 MeV and to get the strongest upper limits on fast radio bursts associated neutrino fluences up to 50 MeV. Recently, BX has searched for neutrino events in correlation with GW events from 2015 to 2020 using the BX data-set of the same periods. The strongest upper limits on GW-associated neutrino and antineutrino fluences have been obtained in the (0.5-5.0) MeV neutrino energy range. The present contribution is aimed to describe the analysis procedures and the deduced upper limits for all neutrino flavors.