I don't know what it is with birds and Styrofoam, but that stuff is like crack for them! They'll go right for it every time. You'd think it would kill them, but my birds have eaten a LOT occasionally (Styrofoam cooler left out where free range flock could get it, same for packing around a washer) and they've all lived with no ill effects. I've heard similar tales here over the years. Your birds will be fine, just pick up what you can find and try to keep them from more.
related story--I worked in a nursing home for years. We often had fish for meals. One patient's husband brought in what he thought was a bottle of lemon juice to go on her fish. It had been there for a month or more before an aide really looked at it and realized it was a bottle of Miracle Grow concentrate! So, I called poison control, they laughed and said Miracle Grow is non toxic, I guess they get calls from toddlers eating the stuff all the time and it's not a problem.
So, my patient was fine, and your birds will be also!