They are pretty interchangeable and have quite similar meanings.
I would use "involve" more so when referring to activities:
*This job involves working overtime hours.
*The politician was involved in a sex scandal
*Get more involved in class by asking your teacher questions.
"Consist" and "include" are pretty much the same, and is used when listing parts of a whole:
*That protein shake consists of many vitamins and amino acids to help build muscles.
*The group consisted of many people of varying ages and gender
*This cake consists mainly of sugar and honey
*The emergency pack includes a flashlight, energy bars, matches, and other items.
*I included an apple in your lunch bag
*The starter kit includes a small bottle, sponge, and manual
Note: You can use "include" as a verb, as you can see above