May I ask why your father is determined the budgies be out of the house by Monday?
Keeping them outdoors the cage you've described is really not a good option.
There are too many things that may happen -- a cat or dog could knock the cage over, the budgies may become overheated, etc.
Will your father allow you to keep the cage in your room or in a separate room in the house he doesn't use?
If not, could your boyfriend possibly keep the birds at his place until you move in together?