The problem is you have an odd number of birds, and you are trying to breed with more than one pair of birds in a cage. For breeding, you should only have one pair per cage, and each pair should only have a single nest. It needs to be the right type of nest, hung as high as possible in the cage – preferably a corner – leaving just enough room for the birds to sit on top of the nest. The male likes to sit there to guard his nest. Breeding birds are territorial. It’s possible the hen is using the nest, and the other hen is throwing the eggs out of the nest. You need to remove the single bird and all of the extra nests, and the pair should do better. They need a private area with little human contact. It’s also possible you have the wrong kind of nest. Most finches prefer the type that look like a hut with one entry hole. It should be woven from natural material – they generally do not like the plastic nests. They definitely don’t use the open type nests – those are for canaries. You should provide nesting material that is sold for finches, and not grasses or anything else you collect outside.
Thank you for asking Lafeber,