First, they are all non-strict. That has a particular mathematical meaning related to functions, but, basically, means they are computed on-demand instead of in advance.
Stream is a lazy list indeed. In fact, in Scala, a Stream is a List whose tail is a lazy val. Once computed, a value stays computed and is reused. Or, as you say, the values are cached.
An Iterator can only be used once because it is a traversal pointer into a collection, and not a collection in itself. What makes it special in Scala is the fact that you can apply transformation such as map and filter and simply get a new Iterator which will only apply these transformations when you ask for the next element.
Scala used to provide iterators which could be reset, but that is very hard to support in a general manner, and they didn’t make version 2.8.0.
Views are meant to be viewed much like a database view. It is a series of transformation which one applies to a collection to produce a “virtual” collection. As you said, all transformations are re-applied each time you need to fetch elements from it.
Both Iterator and views have excellent memory characteristics. Stream is nice, but, in Scala, its main benefit is writing infinite sequences (particularly sequences recursively defined). One can avoid keeping all of the Stream in memory, though, by making sure you don’t keep a reference to its head (for example, by using def instead of val to define the Stream).
Because of the penalties incurred by views, one should usually force it after applying the transformations, or keep it as a view if only few elements are expected to ever be fetched, compared to the total size of the view.