I wouldn't necessarily say that intelligent means educated. (And vice versa.) Intelligence to me is a more general umbrella term for a variety of qualities such as cleverness, insight, education, oranization of thought, etc. An uneducated person could certainly be intelligent, such as the Indian mathematician Ramanujan.
"Clever" to me implies a creativity of thought, especially related to problem solving. It seems to connote some idea that relates to action, such as developing a more economical way to perform a task that previously was more complex and time consuming. A clever new way to clean the windows. It wouldn't be completely out of bounds to talk about "developing a clever new way to think about the poems of Emily Dickinson" but it would sound better to me to speak of "developing an insightful new approach to understanding the poems of...."
Crafty is a bit like clever but it implies a certain deviousness. A clever accountant gets a good tax return for you without fear of breaking the law; a crafty one might just be bending the law a little bit.
"Smart" to me seems to be pretty much synonymous with "intelligent." The only difference is the latter would dominate at the top end of the scale in terms of gravitas or brilliance. For example, which would you use to describe Albert Einstein or some other Nobel Prize winner, "very smart" or "highly intelligent"? As another example, if you were a high school teacher and you had two students, both of whom made straight As in all subjects, but only one of whom exhibited surprising creativity, originality and insight on a regular basis. I'd say the latter is highly intelligent or brilliant, whereas the other would be smart or very smart.