One of the greatest limiters to freedom in public speaking is our self-consciousness and self-judgement. It will be difficult to coax "vocal variety" or "volume" out if you are trapped inside, suffocated by years of negative self-talk.
Getting up and trying to speak with words will be difficult if getting up at all is already difficult for you. Exercises can help. With exercises, word content is removed or unimportant, in favour of free expression, physically or vocally.
The first is a video of Amy exploring improvisational body movement, as she says, "After a hard day the other week, I turned on some music to dance through my stuck places, to get out of the brain and into the body."
Continue warming up by continuing to move your body and introduce deep breathing, tones, facial massage, and over-enunciating.
In this video, Amy introduces us to Polyglot, a contemporary ballet production by Charles Anderson, that combines the spoken word. Pay attention starting at 3:12 when she warms up her voice in her dressing room. Part of the purpose of warming is to shed the self-consciousness and get into the performance.
In this short one from LynnLevity, Lynn demonstrates chanting vowel sounds. When toning, be mindful of your breathing. Notice the source of your vocal resonance. Try moving the resonance around your body. Just experiment, play and notice. You can do this exercise anytime, almost anywhere. Just check with your co-workers first (wink).
Now let's ramp it up by adding words. Improvisation games are a great way to practice getting out of yourself. "Change Emotions" is just one of many improv exercises. At the tone, the actor will change emotions. Watch as the fellow on the right actually turns red as he expresses extreme frustration.
Yes, this scene will not win an Academy Award, but that's not the point. The point of improv is for one actor to offer something, the other receives it (requires listening and thinking), and augments it to return the offer. In this exercise, it's all about expressing the emotions in an exaggerated way - getting out of the self - liberated from the chains of your ego trying to keep you safe.
If your public speaking is hindered by shyness, stiffness, self-consciousness, emotional inhibition, or you otherwise struggle to get out of yourself, put public speaking aside for a little while. Experiment and play with exercises in body movement, voice, and improvisation until you no longer care what people think... until you no longer care what you think.
As Amy might say, Get out of your head and into your body.