Hi,
I have been breeding budgie as a hobby for 2 years now and have had to raise several babies at once. It is hard and can have complications. It was particularly difficult as I have to go to school therefore they had no food during the day so I had to fill them up before I left and feed em again when I got home. Don't give up on the parents, they still yet may come back. But in the meantime, those babies need you!
You do need to purchase budgie hand rearing formula from your local pet store or produce place. I always have some on me before I breed just in case something goes wrong.
Most hand rearing formula packets have instructions on how much you feed the babies each day, how much water to add. Ect. But I will let you know what I do,
As your babies are 3 weeks old they are close to fledging so they are on a more 'thicker mixture'.
The formula has to be warm but not too hot. If it goes cold or the babies go cold then the food sets in their crop (where food goes, on chest) and it does not digest therefore a very ill baby. Like all babies they are always hungry. You don't need a schedule on when to feed them you simply feed them till their crops are full and then wait till it is empty and repeat. I didn't have a syringe to use for my babies, I just used a spoon. Your lucky really, to have these babies at 3 weeks and not 1 week and they don't need as much warmth or care as a younger budgie. As for the formula, it should come in a powder form, but there are some that are already mixed and ready to go.. I have the powdered one, that you mix warm water with. I usually gage on how much I should put in as I add some water and mix and see if the thickness is about right.. You will know if they do not like it or it is too hot. But they will have to get used to the formula as it would taste and feel completely unnatural for these three bubs. If you have any other questions. Ask away, I have reared and successfully raised 11 babies throughout my breeding experience. Some I have hand reared just because I wanted them super tame! Which they will become as you are their mum now.
Hope I have helped.
Good Luck. Hopefully the parents return and all is back to normal!