Hi Nicki,

If the squash tastes bad (usually really really bitter), it might make you sick. There are some varieties of squash that are super bitter, but even those are unlikely to make you nauseous, unless you consume a lot. I lived in Bangladesh for a few years and that had a bitter squash that like to eat with curry. It took some time to acquire a taste for that, yet, I survived. 

Your squash looks like they may not have ripened properly. Hard to tell without touching and tasting. Did it run out of water, time, or were there animals eating on it? Animal graze will often arrest development. Do you know the variety? Looks like some sort of butternut or buckskin type. Where did the seed come from?