Yep, what matters is momentum in these cases. Photons have momentum. They do not have rest mass because they only exist as movement of electric and magnetic field, and as such when they "stop" they are destroyed*, absorbed by matter in most cases, and their momentum is conserved.
As far as dangers of radiation go, all forms of radiation can be dangerous but with proper protection, it takes a lot for it to become a threat.
Ionizing particle radiation (alpha- and beta radiation)... not a threat externally, rather damaging when the source is ingested or inhaled or concentrated into some organ like thyroid gland. From outside, they are peanuts; alpha rays are stopped by few inches of air or the dead surface layer of your skin; you could wear a ring with alpha source in it for all your life and it would hardly do any damage at all.
Beta- particles are not a threat as such either; they stop by about dozen metres of air, or a wooden wall or plexiglass... however, beta+ particles are another matter because when a positron hits an electron, it causes annihilation and consequently creates two gamma photons of 511 keV, which means that practically all beta+ sources with activity of A could be considered beta/gamma sources with activity of A+2A (one A from beta activity, two further A's by gamma radiation induced by annihilation).
Gamma radiation... penetrates well, but like already said, that also means that majority of the stream of photons passes through your body doing no damage whatsoever, which means that if you have ingested an alpha source of activity A and gamma source of same activity (decause per minute)... the exposure you get from alpha radiation is a LOT bigger because every single helium nucleus hits your tissue and ionizes stuff and causes a lot of damage, whereas only a scant percentage of gamma photons hits anything within your body, most of it passes through. For a dangerous dose of radiation resulting from exposure to gamma rays, you need a really hefty exposure at high intensity, and that kind of occasions are really rare. There's also the fact that gamma radiation like other forms of EM radiation weakens in the inverse square of distance, so when you double the distance, you get quarter the exposure, which means gamma radiation is really a concern only in the immediate vicinity of high active source.
So.
Problems with radiation arise when:
-gamma radiation source is so intense and close by that the dosage grows big enough even despite the low dosage/exposure ratio. This is usually only a problem with really high active nuclear waste, or direct exposure to nuclear reactions. In which case there are usually more pressing matters to be concerned of, like the building collapsing on top of you or the glowing sludge proceeding towards you.
-alpha- or beta sources are ingested, inhaled or otherwise introduced to your body internally. This is the main hazard of ionizing radiation because gamma ray exposures of hazardous level simply don't happen that often. A nuclear bomb explodes, releases a burst of radiation (including radio waves, microwaves, visible light, thermal radiation, X-rays and gamma rays), and then that part is over with. But the explosion also vaporizes a lot of alpha and/or beta-active nuclei, both actual daughter nuclei from the fissile material and nearby matter affected by the neutron flux. This fine mix of stuff is spread all over the place and forms the so called fallout, which causes at least as much problems as the actual material destruction since it contaminates the food and water sources and the very air you breathe and it can cause a radiation poisoning all by itself without any contact to the actual explosion, not to mention the increased risk of cancer and deformations on growing fetuses...
Now then, neutron radiation.
Is not a real threat for the same reason gamma radiation is not really something to concern yourself with; when you're in strong enough neutron flux to cause problems, you'll have other things to think about... but not for long. Neutron radiation is basically only caused by nuclear reactions, not by nuclear decay. Spontaneous fission can cause this, but that's a very rare form of decay and rather insignificant compared to alpha, beta and gamma decay, so it can be considered to only be caused by fission and fusion reactions.
Now, neutrons aren't too bad by themselves. They are heavy, they have a varying amount of momentum depending on the source reaction (slow neutrons and fast neutrons), but they have no charge at all so they don't easily interact with negative electrons or positive nuclei. So they have a reasonably good penetration. The best shielding would be a material with as high nucleus density as possible. Lead is pretty good for this purpose. They also have a half time (or average life span) of about three ten minutes. The problems arise when they happen to hit some nuclei, because that basically converts the nucleus into another isotope which may or may not be unstable, and that means you end up with alpha/beta/gamma sources within your body.
It also is the reason why nuclear reactor parts end up radioactive, as well as some changes structural integrity as, for example, Fe-56 nucleus gains three neutrons it changes into Fe-59 which is an unstable isotope with half life of 44 and a half days, and decays into cobalt, which has different mechanical properties than steel. Of course if Fe-56 happens to gain four neutrons it will decay into Co-60, which further decays into nickel...
So yeah, all forms of radiation are dangerous, but all in different ways, and they can be dealt with in a way that largely neutralizes the threat from them.
The biggest exposure you'll likely get is from bad ventilation on regions with a lot of radon released from the soil... and background radiation in general.
*This is a fundamental interpretation of Maxwell's field equations - electromagnetic wave motion can not exist in frozen state; it is also the logical basement on which Einstein laid the Specific Theory of Relativity (speed of light is always observed constant).
