All three are used in different situations, Curios describes your strong desire to know, Eagerness tells you about your excitement whereas, Anxious describes your worrying condition. Curios: Strong desire to know about something. Usage: "they were very curious about the people who lived in the caves in past. It could also mean strange or an unusual thing. Usage: "Curiously enough, a year later exactly the same thing happened again. Eager: Interested and excited by something that is going to happen. Usage: " Everyone here on italki seems eager to learn:)) Anxious: Feeling worried or nervous. Usage " Parents are naturally anxious for their children". It could also mean, wanting something very much. Cheers:))

You can look them up in a dictionary. http://dictionary.cambridge.org http://dictionary.reference.com/ http://oxforddictionaries.com/