Very informal. I found out about the position in person. I had a phone interview (about 30 minutes), and an in-person interview was scheduled to follow in a few weeks' time.
It was all-day. Had to present some of my research from my PhD, and had one-on-one discussions with several other postdocs and staff members. Also got a tour of some facilities. They paid to put me up at Argonne guest house, and also provided per-diem and covered travel to Argonne. Did not get really grilling technical questions, or any useless behavioral interviews. Everyone was very welcoming and respectful, and were eager to market what Argonne had to offer.