Not sure about neutrons. Gammas, or x-rays at least, could come from bremmstrahlung.
Alpha particles will produce secondary radiation occasionally when they hit light nuclei. The oxygen in the Pu oxide is almost entirely O-16 to minimize neutron production.
Possibly Pu-239 or other impurities.
All U and Pu isotopes undergo spontaneous fission, producing neutrons and random daughter products.
Some very small portion of Pu-238 will eventually pass through Tl-210 -> Pb-209.
Where are these gamma rays and neutrons coming from? The decay chain for Pu-238 is via alpha emission (Pu-238 -> U-234 -> Th-230 -> ...) which won't penetrate the casing.