An Examination Under Oath is basically a deposition. However, whereas a deposition is a product of a court rule because there is pending litigation, an EUO is the product of contract before litigation is filed. In fact, in almost every policy, you cannot initiate litigation against the insurance company until the EUO process is complete. If you fail to satisfactorily complete the EUO process, the insurance company will be able to shut down your law suit fairly quickly. Thus, it is a very important process that should be taken very seriously.
Much like a deposition, the EUO process generally consists of two parts: 1) a request for information and 2) questioning under oath. The request for information will likely be quite burdensome and may be done before and after questioning. While most EUOs start with a request for documents followed by questioning under oath, the insurance company can go in whatever order they want. You can be questioned multiple times and other people associated with you such as your wife or other household members may also be questioned.