儿童 and 小孩 are similar and refer to comparatively large range of age, generally from 3-12. However, 儿童is usually used in formal occasion, e.g. law and title of institution related to children. 小孩 is more occasional. You can hear this word in daily conversation of people.
幼儿, on the other hand, refers only to small baby that is under the level of primary school, including new-born baby. For example, 幼儿园, which is kindergarten.