My 7 week old puppy projectile vomited these little white worms. They are so gross and wound themselves up into these little balls. The pup is the runt and the other 2 pups are much bigger and heavier. They have all seemed healthy and active till today. Anyone know what kind of worms they are and any home remadies

You took the responsibility on when you got pets... take the reponsibility to take them to the vet as needed rather than take the cheap way out.

They need a vet to take care of these worms... and you better do it to all the dogs and do it soon because it's possible that you could get the worms as well.

This isn't something to play around with. You have a responsibility here.

There won't be any home remedies and all of your pups probably have intestinal worms, and they have been known to work their way up to the throat. You had better take a stool sample to the vet with you and have them all deformed.

Why are you breeding if you don't plan to do so responsibly?

Part of breeding is making sure that the puppies, and the parents, get the care they need. Have they had their first set of shots and de-worming yet? If not, it's time to go in and get them checked, and vaccinated, before they go to their new homes in a few weeks.

Most likely roundworms, they resemble a piece of spaghetti. Take a sample to the vet for testing to be sure. You'll need accurate weights on EVERY dog in your household and the proper dewormer from your vet for each dog. Don't trust any home remedies that you may hear about. And don't trust what you pick up at the supermarket or department store. All puppies are born with this parasite already installed.
While you are there you need to discuss the importance of vaccines and a good deworming protocol.
And, yes as Odinn mentioned there are some parasites that can transfer from your dog to you or your children, in particular the roundworm can migrate into your eye, so hand washing and cleanliness will be very important.

Make sure you let your vet know about any other pets you have in your household. Our puppy had worms at 10 weeks old and we had to treat our dog and our cat.