I'm glad to hear your birds are doing better. Please remove the nest box immediately. Budgies do not need hidey houses or boxes to sleep in and having a nest box or anything that resembles it will encourage accidental breeding. Additionally it seems your cage is below the minimum size for 4 budgies. The minimum for two budgies is 30 x 18 x 18 inches. Have a look through all the stickies and articles on the forum to ensure you are giving your birds the best care possible. I've linked a few down below for you.
Essentials to a Great Cage
When We Don't Want Eggs!
A Heartfelt Plea to All Members
A Healthy Diet for your Budgie