You have to understand what fumes are, and why you smell them.
The smell is from VOC: volatile organic compounds. The lower the VOC, the less it will smell. Cheap paint has a high VOC, and expensive approaches 0. It's "volatile" because it evaporates quickly into the air, hence the smell. "Organic" because it contains carbon. And "compound" because it lots of stuff making it. Different paint colors and consistencies demand different things.
VOCs can react with people and things. So, depending on every aspect of the paint (brand, shade, etc), it could, in theory, act as a solvent on the bonding agents of the disc. Or adhere to the clear polycarbonate, causing it to cloud over, thus being difficult or impossible to read (maybe ever again).
Inhaling a VOC is not good for your health.
Who paint the house? It sounds like dirt-cheap crappy paint was used. Honestly, I'd paint back over it with low VOC paints. It will seal in the stink. But you also run the risk of the old layer not curing, if it's so new that it still stinks.
https://toxtown.nlm.nih.gov/text_ver...cals.php?id=31
That situation stinks!
FYI, I didn't buy a house back in 2007 for this very reason. Not only did it stink, but it was sticky.