Sunlight and air are your best friends here. Put them outside again. If there's a breeze, it will help. You might also try putting the sheets in a clothes dryer on high or medium heat for 30 minutes.(Don't use scented dryer sheets) The heat, air circulation and tumbling may help. Good luck!

I've encountered that particularly smelly pvc packaging and have yet to find a solution. Washing seems to set the smell. These days I try to check first and won't buy anything if the packaging seems very smelly. The smell from pvc is from the plasticisers and some of them are toxic and are being phased out. I commented on the problem to a saleswoman in a manchester store once and she said she airs her sheets before washing to get rid of the plastic smell. I would not put new items in the dryer, especially on hot, that would just spread whatever is in the new items around the dryer (don't forget they also have chemicals in them to protect them during handling and storage prior to being bought). In one of my experiences (before I knew about airing first) I washed the inner sheet and pillowcase first and had no trouble, then washed the outer sheet which had been touching the packaging and it reeked. I had them all hanging on the line outside for days and not only did the smell not come out of the one sheet but it spread to the other sheet where they were flapping against each other. I haven't had the time to persevere with those sheets so I'm sorry I can't tell you what works, especially after the item has already been washed. I'd be inclined to return them and tell the manufacturer why. In an era when we are becoming more aware of the problems of plastics it is ridiculous that manufacturers are still using smelly pvc which contaminates the contents and then ends up in landfill instead of the safer types of pvc or better yet the biodegradable/recyclable alternatives like cornstarch based plastic or good oldfashioned cellophane or cardboard.