Quirkily is the “in that way” form of quirky. It says that someone does something in an unusual way — not broken, not ugly, just a bit off the usual path, and often in a way people rather like. You put it with a verb: she dresses quirkily, the room is quirkily painted, he smiled quirkily. It is a warm, slightly playful word. Writers use it for clothes, rooms, films, and little habits. It is not a school-formal word, and it is not a medical word for “strange.” Though actually, it can be a polite cover: people sometimes say quirkily when they mean weird but do not want to sound unkind. The feeling is “odd, and that is the charm,” not “odd, and that is a problem.”