What kind of radiation do supernova remnants emit? Do supernova remnants emit EM radiation? Moreover can neutrinos be emitted by these remnants?
Young supernova remnant release a substantial amount of radiation as they expand into the interstellar medium. In the free expansion phase, the outgoing shock wave heats up matter to $\sim10^6$ Kelvin, producing thermal x-ray emission. Throughout their lives, the remnants are responsible for quite a lot of non-thermal emission, including synchrotron radiation from relativistic electrons. This synchrotron emission stretches throughout the electromagnetic spectrum, including at radio frequencies. There is, additionally, non-thermal gamma ray emission through several mechanisms, including inverse Compton scattering and hadronic interactions.

Supernova remnants are also thought to be one of the main sources of galactic cosmic rays. Protons are accelerated through the shock front to energies of up to a few petaelectronvolts. Cosmic ray production may be associated with gamma ray emission if there is additional dense gas for the cosmic rays to interact with.

This brings us to the final point of your question: yes, supernova remnants are responsible for some neutrino production. Those cosmic ray/gas interactions produce (in addition to those gamma rays) neutrinos through hadronic channels and the decays of short-lived intermediate particles, including pions and kaons. This also means that probing the gamma ray spectrum of a supernova remnant can tell us something about its neutrino spectrum.