What your teachers seem to be suggesting is great - definitely use a thesaurus.
Apart from that, keep a word bank. I used to carry around a notebook for whenever I came across new words. Read other people's essays and pick up on new vocab and phrases and different ways of saying the same thing. Language and expression is learned through imitation.
Read books, Stick! Read for your pleasure. If not for pleasure, then read for the sake of your education. You'd be surprised on the words you might not have come across before and the terminology you can add to essays.
Oh, and annotate your school texts. Don't be anal about the resale price; the person who buys the book will probably be more appreciative of your wonderful insight . Underline key words that jump out at you, scrawl comments on the margin, highlight quotable passages. Key words and expressions I could use in essays often form in my head during these readings. (I'm doing this with The Quiet American just now

) Basically, your expression evolves from reading the text.
I would also suggest thinking carefully before you write an essay. I write far more notes on concepts and plans than actual essays. Essays are more a distillation of ideas and phraseology. The problem with essays is that you're aware that everything you write is going to be judged and this can often stunt expression. In your notes, however, you can experiment with your thoughts without this extra pressure. If you're finding it difficult to fully capture your expression, I would recommend free-writing and fully exploring your thought process first. Once you have some flow going, expression becomes easier as you learn to write in sync with what you are truly thinking, regardless of how it fits in a paragraph, or whether it aligns with the contention of your paragraph or whether you think your teacher agrees with you or not. You can sort that stuff out later. For now, just write without judgement. Pick a prompt and just go with it. Don't look at what you've written until you've got a couple of pages down. You'll be surprised at how much your expression improves, or the turns of phrase you discover that you didn't think you were capable of. It is only in the next step that you cull all the unnecessary information, decide which parts to keep and fit your ideas into a practice essay. Once you've done that you can just continue refining your ideas in practice essays.
The rest is just practice, Stick, and I'm positively certain that you, of all people, are practicing.