How do I learn to speak more eloquently?
Reading will help with this, especially reading well written books by authors with a reputation for eloquence. English is often spoken quite differently than it is written, though. So be careful you don't start sounding overly stilted or contrived.

Eloquence can be taken too far if it is your main objective. If your goal is to teach people to speak English, you would be better to concentrate on teaching them to speak in a way that helps them communicate well.

I, personally, use filler words too often, as well. It takes some concentration on what you want to say and how best to say it, to make progress with this. That, and a good vocabulary, so you will have many words to chose from and the experience to know which word would be best to chose. This just takes practice. Take every opportunity to converse with educated native English speakers and listen carefully to how they speak.