The main issue here is that you can’t breed cockatiels with an extra bird in the cage. You should only have one pair in a cage for breeding. Even if not breeding, it’s not a good idea to have an odd number of birds together. While they may seem to get along OK, what will eventually happen is two birds will bond and the extra bird gets bullied. Most likely one of the males will finally decide to establish dominance and claim the female for his. He will then get more and more aggressive with the extra male and if not separated, he is likely to kill it at some point. This type attack can seem to come out of nowhere, so the best thing to do is remove one of the males now. You should also go ahead and remove the nest box for now, because you shouldn’t put up a nest box until a pair has formed a mate bond. Occasional mating doesn’t count. And if these birds aren’t at least 2 years old, they should not be paired yet at all. A female under 2 is at a high risk of becoming egg bound. And both birds are really not ready to settle down and take care of eggs and chicks. They are likely to develop bad breeding habits that will ruin them for ever being good breeders. Young birds are normally more interested in mating than caring for eggs. If these birds are under 2, that definitely explains why they have not really bonded and just mate from time to time. A young male will often destroy the eggs or eat them because he wants the hen to mate again.
If you are serious about breeding, leave one male with the female and wait to see if they seem to bond. If they don’t, try the other male. If they bond, and both birds are over 2 years old, you can install the nest box again. You should attach it to the outside of the cage, as high as possible. The birds need to be eating a nutritionally balanced diet like pellets or our foraging diets – a seed mix does not provide the nutrition they need. Also offer dark, leafy greens, chopped veggies and some fruit. Once you give them the nest box, start feeding them some egg food daily. This can be a dry commercial egg food or cooked egg with the shell washed, crushed and cooked with the egg. This should be fed daily before egg laying and until any chicks are weaned. If they do have eggs or chicks, the nest box has to be removed once the chicks are weaned and the pair rested for 6 months. You need to do this every time. They should be limited to two clutches a year, which is one more than they would have in the wild. Any chicks need to be removed as soon as they are weaned unless you hand feed them. You should never allow related birds to breed. But do not put the chicks with the extra male. You would need to wait until a chick is 2 years old before introducing it to the extra male.
As for the eggs she has right now, it is probably best to discard them. Eggs incubated on the cage floor rarely fare well. And you can’t have the 3rd bird in the cage if she is sitting on the eggs. She will get aggressive when nesting, as will the males, so there will be fighting if you let her sit on them without removing the extra bird.
Thank you for asking Lafeber,