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I read an article that said you should avoid certain words in writing such as really, you, feel, think, as, a lot, sort of, kind of, like, just, used to.

I think the intention is to be more direct and succinct.

My problem is not so much my writing but the spoken word, I'd like to improve my spoken vocabulary by replacing common empty words or phrases with more intelligent descriptions.

But what words should you replace them with without sounding pretentious?

Is there a valuable guide out there on the interwebs that would help someone improve their speaking skills in this manner?

I would add to Leon's answer, a short, concise essay by George Orwell that will do wonders for your writing and critical thinking skills: Politics and the English Language. It is routinely cited as an authoritative text for academics to stop writing gibberish from overuse of academic jargon and would seem to fit your need nicely. While Orwell talks about political discourse, this example really can be extrapolated to almost any discipline. It addresses your points on empty phrases and coming off as intelligent and direct without being pedantic directly. You can read Orwell's Politics and the English Language here

Enotes summarizes this important essay as follows:

“Politics and the English Language,” though written in 1946, remains timely for modern students of language. In this essay, Orwell argues that the English language becomes “ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts.” To illustrate his point, Orwell cites writing from two professors, a Communist pamphlet, an essay on psychology in Politics, and a letter in the Tribune. All these examples, Orwell argues, have two common faults: staleness of imagery and lack of precision. In his follow-up analysis, he discusses general characteristics of bad writing, including pretentious diction and meaningless words. His purpose in the analysis is to show “the special connection between politics and the debasement of language.”

Also you can try reading this webpage on a regular basis which explores similar themes.

Firstly, the advice that you mention concerning the improvement of writing by the avoidance of certain words has little relevance to improving speaking. Many of the words you list are fillers that play an important role in spoken language - although of course it is possible to overuse them.

But are you asking here about everyday conversation? Or are you thinking of specific contexts such as meetings at work or giving a speech? You are certainly going to sound pretentious if you ask your wife "May I request your assistance in the garden?"

That said, the best advice is just to increase your vocabulary naturally by plenty of good-quality reading and by listening to (e.g. TED) talks by presenters whose eloquence you admire. You will then have an increased lexicon to work with.

But any obvious straining to sound sophisticated is almost inevitably going to come across as pretentious.

There are many ways you can improve the clarity, concision, cohesion, and depth of your spoken discourse. Here are three techniques I particularly recommend:

Firstly, and most importantly, get to grips with Aristotle's 10 Categories of Being.
As a starting exercise, use them to describe a living thing at a particular point in time and space. See my TEDx talk on them here.
They will give you a framework that will help you think more precisely, and you will have a motivation to find the words and phrases you need to express those more precise thoughts.

Secondly, think of 3 things (adjectives or nouns) to say about an object (noun) and something about the object (predicate) - keep it simple. For instance:

The small, gold, fountain pen is on the table.

or

Rusty says he's not happy with the Stack Exchange approach to combining forum, wiki and FAQ interfaces.

Then expand the sentence into a paragraph with a clear topic sentence, body section, including signpost words (e.g. firstly, secondly, finally), and a clear conclusion.
(Some people refer to this as a 'hamburger' paragraph). For instance, the first example could be expanded as follows:

There are three things I particularly like about the
pen on the table in front of me right now: firstly, it's gold, and I find the way it reflects the light
rather beautiful. Secondly, it's small - small enough to hold
comfortably, but not too small that it disappears in my hand, or feels
insubstantial. Finally, it's a fountain pen - the ink flows smoothly
and it's a pleasure to write with. All in all, the combination of
those three things make it one of my favourite pens - it's an
inspiration to write with.

I suggest you try expanding the second, noun-based example yourself.

Finally, slow down. Here's an example of how a simple yet deep thought can be communicated clearly and effectively when delivered at a thoughtful pace, with clear signpost words:

Bertrand Russell's 'Advice for Future Generations'.

The point of all of these exercises is to help awaken imagination, inspiration, and motivation in you, to deepen your experience of the world, so you can communicate that depth to others and wow them. Follow the advice above, and you'll be well on the way to doing just that.

[Did you notice how I used an expanded 'hamburger paragraph' approach to structuring this answer? What was the effect it had on you?]