You can store the strudel at room temperature, and it will last for 1-2 days. Pastries tend to dry out fairly quickly, so they don't stay fresh for an incredibly long time. Another option is to freeze the leftovers. Wrap up each one with a piece of plastic wrap and put them in a freezer bag or container. They will last one to two months in the freezer and can be reheated in the microwave.