I ran a measurement lab in Surrey during the Chernobyl crisis and carried out whole-body measurements of many people, including bus-loads of school children returning from the general area.
What I detected was primarily "U235 fission fragments" (Google the quotes) which are the unequal sized 'halves' of 235 - lots of mass numbers around 90-100, lots around 130-140. The people that were contaminated had been caught in the rain or walked in puddles. The rain took particles into their hair which lodged in the microtexture of the hairs themselves. These don't wash out easily and had to be cut out. The nature of the particles suggested that they were smoke from a very intense fire that was able to volatilise the normally refractory isotopes of Cerium and similar. When these cooled, they picked up other nuclides including I131 and Cs134 and Cs137. Whole body counts after showering and radioactive hair removal detected very low levels of thyroid uptake.
Later I had the opportunity to count the levels on MSC filtration systems. This was interesting but I never got a satisfactory answer. The filters are 3 stage, prefilter that removes coarse dust from the air, a fine filter that takes out most of the rest and a HEPA (High Efficiency Particle Absorption). The main nuclides that I was looking at were Iodine and the Caesiums. I found that the ratios of Cs134 to Cs137 were different between the different filters, but consistent in different parts of the same filter and between filters of the same type. I could only conclude that the different particle sizes came from fires of different intensities in different parts of the reactor. These different parts may have had fuel rods of different ages explaining the different Cs ratios.
I was also asked to count the contamination levels on samples of herbs and spices imported by a friend of my Professor from different countries that had different exposures to the radioactive clouds. Sage in particular was contaminated, presumably because the furry leaves collected particles in a similar way to human hair.
The Caesium issue was thought to be a biologically transient one. It was expected that any that was absorbed would be flushed out of the body along with potassium (sodium has a specific mechanism to reabsorb it if required). This was found not to be correct and Wales had a long-lasting crisis because the caesium was remaining in the soil, reappearing in the grass and being taken up in sheep. Some farms were not allowed to sell their sheep for years.
Gamma-neutron reactions require a gamma energy in excess of 6MeV - rare in reactors.
Fission continues in the reactor to this day. U235 is spontaneously fissile, and alpha particles from the fuel rods will generate neutrons if they interact with low-Z elements. These neutrons will stimulate fission in turn.
Neutron activation is a problem. Gold jewellery or fillings are not permitted in staff in a nuclear facility because the cross-section fot gold is so high. Other substances are also easy to activate - steel invariably contains other transition metals, especially Cobalt. That becomes activated into Co60 in even a mild neutron flux. Fortunately not particularly fast.