I have not used any of these with my kids, but I own them all, for whatever that is worth. I think I would do Lively Art first, because it is a good introduction to essays – the structure, what it’s for, how to come up with a thesis statement, etc. I would follow that with Power in Your Hands because it focuses more on types of essays and how to write each type (among other things like devotions and newspaper articles).
As for Elements of Style, I have heard it suggested that a student should read it each year of high school, since it is short and contains lots of little rules that need repeating, but honestly, I can’t imagine making my kids read it. They would probably die of boredom. I don’t know why, but my boys just can’t handle reading about writing. LOL