I am sorry to be late in answering your question. It's already 9 hours since you posted it.
The classic thing to do with any dog who has eaten something they shouldn't and has diarrhea and vomiting, is to restrict all food for 24 hours. Small amounts of water should be given very regularly (every half hour or so) to prevent dehydration.
The next day, give the dog only a small amount of plain boiled rice. See if that stays down. If it does, give more, a little every 2-hours or so. If at the end of the 2nd day all seems well and the dog seems recovered and hungry, then do some plain boiled chicken or white fish (search the fish for bones!! Dogs don't need fish bones!) and give that with the rice. Same the following morning, and then gradually re-introduce their usual food over the next couple of days.
This will work with a simple tummy upset.
But the most important thing is -can they keep down the water? If they vomit up water then they need the vet. The best solution is to put them in an IV fluid drip.
It is also possible the fish oil was contaminated, in whch case they could be infected with a bacteria.
There is nothing wrong with an Omega-3 supplement for most dogs. But there are also some who are highly sensitive to anything fatty and can develop pancreatitis.
My own advice? See how they go with the water. If you can't get water to stay down, or if symptoms persist, go to the vet a.s.a.p.