Hello Emil and welcome!
You sure are a ways from home! What a great opportunity you have in front of you. There are lots of ways to go about earning a bird's trust and taming it. It will take patience and lots of time. How long are you staying in the US? If you're committed and are staying here for a while (a few months?), I don't see why you couldn't tame these budgies in your host family.
You can use positive reinforcement to train the budgies. All that means is, rewarding them when they do something you want them to do. As in, offering a treat on the side of the cage and waiting for them to approach and take it from you. The idea is to show them that good things happen when you are around.
Be sure to check out the different sub-forums here, there's tons of information here and many experienced parrot lovers from all around the world.