Even the stuff that seems odorless and non-toxic can be harmful. Epoxy, which most think is harmless, can also be harmful. Some resins are just toxic (like polyester) and will cause damage right away. Others may cause problems from exposure over time.
No one knows for sure (or will equivocally state) exact what might happen to you as that would be cause all sorts of marketing and liability issues.
Don't let any resin touch your skin while it's still uncured (i.e. in liquid form). Not only are fumes harmful (whether you can smell them or not) but you can get skin irritation, possible poisoning, or develop a reaction over time, through contact with your skin. Always wear some sort of protective gloves when working with it. This includes when sanding to keep the dust off your skin.
You should not breathe fumes emitted by curing polyurethane or epoxy resins even if you can't smell anything. You can develop a sensitivity over time, which means everything could be fine but then one day you will have a nasty reaction. Once that happens, you won't be able to go near the stuff again.
Never breathe dust generated by sanding any resin. Always wear at least a dust mask, though I now wear a NIOSH-approved respirator whenever I am working with potentially harmful compounds (including resin, epoxy, CA, solvents, paints, and sanding dust).
I was also guilty of working with stuff without protection in years past. There is no way to know for sure what the potential long term health effects can be. For sure, a lot of what we modelers use can cause cancer. Some chemicals can also cause BRAIN DAMAGE. That's not worth taking a chance, so better safe than sorry.
Now, what were we talking about again? LOL :lol