The neutron is not an elementary particle. Its overall charge is zero, but depending on the energy available the fact that it is composed out of charged quarks becomes important. Thus both the strong force and the electromagnetic will play a role depending on the energies of the scatters and the targets.
For low energies , like the ones coming from fission reactions in reactors, matter is practically transparent to the neutrons due to their zero charge, and in order to absorb and contain them a lot of matter is needed. They can interact with the strong force with the nuclei of the atoms, be captured etc, generating secondary radiation centers.
Due to the quark structure the neutron has a magnetic moment that can interact with magnetic fields.
To interpret correctly the crossections the quark nature has to be taken into account where also the electromagnetic interactions will enter, example here., mathematical models are necessary.