I am looking for way(s) to illustrate these concepts so to help my students understand them (and not just calculate them for various distributions, which is what is often done in class).
Buse, A (1982). The Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note. The American Statistician, 36:3a, 153-157 is an excellent reference with one major reservation: Lagrange multiplier test should have been called Rao's efficient score test. I wrote Prof. Rao about this when the paper came out to let him know my frustration that incorrect terminology was being used and he was thankful. Other than that it's an excellent article. I've sent you a personal email with the pdf.
Another article by Linda Pickle is also excellent - Stat Comp & Stat Graphics Newsletter Nov. 1991 which I'm sending to you.