: How are different writing styles/voices possible? It seems that writing style varies from author to author, and from work to work, but how does the English language allow for so many different

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Because of the phenomenon of combinatorial explosion.
Suppose you know just 100 words. You decide to write a sentence that is 10 words long. You could write 100^10 possible sentences, or 100,000,000,000,000,000,000 -- 100 quintillion. Of course the vast majority of those would be meaningless gibberish; I don't know how you'd calculate how many possible MEANINGFUL sentences. But surely billions or more. And in real life you surely know more than 100 words, and sentences are not all the same length.
You can use common words or technical words. You can use strong words or mild words. You can ask questions or make statements. You can use short sentences or long sentences. You can give detail or be general. Etc etc. There are many ways to vary your tone.
Just for example, consider:

Bob thought that Sally was pretty and he liked her.

compared to

Bob was overwhelmed with awe at Sally's beauty, he couldn't imagine a more beautiful creature existing in the universe, and he determined that he would do whatever it took to possess her totally.

Both are basically the same idea, but the first is short and clinical while the second is verbose and flowery.
Or:

The car failed to start because of vapor lock.
The car failed to start because it hates me.

One is scientific and testable, the other is emotional and subjective.
Etc. One could go on indefinitely with a game like this.

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There are many ways to express the same thought - many more than you might realize.
Vocabulary
The first thing is the difference between active and passive vocabulary, also known as productive and receptive knowledge. You may recognize a word and its meaning when reading it, but you may not use that word when talking or writing yourself. It's just a word that you have used so few times that it wouldn't cross your mind to use this word.
To take an example from a recent discussion here on Writers.SE (How to talk about certain anatomy without sounding vulgar or cowardly?): you may understand the word Gluteus Maximus and what part of the body I am alluding to, but using a medical term in a normal conversation wouldn't cross your mind. Using posterior on the other hand feels more natural, though in general I would probably use butt. Your usage will probably vary. Maybe because you like medical terms, or because you don't like defensive descriptions like posterior.
To cite the Wikipedia article I linked before:

An average 20-year-old knows 42,000 words coming from 11,100 word families

Now you have to ask yourself: how many words are there in total?
According to the Oxford dictionary:

It's also difficult to decide what counts as 'English'. What about medical and scientific terms? Latin words used in law, French words used in cooking, German words used in academic writing, Japanese words used in martial arts? Do you count Scots dialect? Teenage slang? Abbreviations?

It's not that easy to find out how many words there are. And the number changes all the time because people are creating new words and older words are slowly forgotten.
But to give at least a rough idea the link also contains the following phrase:

The Second Edition of the 20-volume Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries.

Using these very simple statistics we can say that the average 20-year-old knows about a fourth of the currently used words in the Oxford English Dictionary.
But you have to adjust this number: the german article about vocabulary mentions that the standard vocabulary contains around 75,000 words - while the total is estimated to be somewhere around 500,000 for everyday conversations. If you are taking into account specialised terminology this number goes up into the millions, with the example of chemistry having probably around 20 million words.
The average 20-year-old may have a pretty good grasp of the normal everyday language and know quite a lot of those words and he may understand a good amount of stuff that he wouldn't use himself, but there are so many more words in the world that he never heard about that it's unrealistic to say that he will have the same style of talking and writing as his peers.
The bottom line is that you are probably vastly underestimating the amount of words that your native language contains. The active vocabulary of you, your friends and your family may be similar, but if you are asking a different group you may find huge differences, just because there are so many possibilities. The same applies to sentence structure and other parts of writing.
You also asked about example - take a look through this answer. I tried to hide a few different ways of speech here.
Did you catch the difference in referring to other sources? In the third paragraph I linked another question and paraphrased the content. Afterwards I changed to citation from Wikipedia and other sites. It's not unreasonable to see this as one part of my voice. Am I using a lot of paraphrasing or citations? Or a mixture? How much paraphrasing sounds good? There are some grey areas here, allowing for different voices if you just compared this simple attribute throughout the site.
Sentence length
The easiest thing to express different voices is through the use of longer or shorter sentences. Look at your own post: I can clearly see that you prefer longer sentences. You used a lot of commas and and's to extend your sentences and except for your last paragraph each paragraph contains exactly one sentence and is at least 1.5 lines long. Your last sentence would only be half a line, which is probably why you didn't bother making it a paragraph of its own.
I also like long sentences. Most of the time, at least. Sometimes shorter sentences are better. They are easier to understand for the reader.
But then again, longer sentences may sound more eloquent, which might be the desired effect when writing. This completely depends on your target audience - are you writing for younger people, who may have problems following long, complicated sentences, or academics who seem to have a knack for this kind of sentence structure?
Punctuation
Did you realize how often I use dashes and colons to split a sentence and at the same time continue the thought? It's an easy way for me to write a pause. At least that's how I like to think about it. And my question marks are often denoting a rhetorical question. You didn't use any of these things. You seem to strive for clear sentences that are specifically without a pause, or use commas to achieve the same effect. You have a very different voice.
None of us has used semi-colons, though, even if they are also part of writing. Think about the many ways you could combine your writing with mine and add other punctuation to achieve different voices.
Examples
Enough with the long walls of text, it is time to show you some clear examples of how you may express the same idea in vastly different form.
This is probably enough. I should switch to the examples. It'll be easier if I show, instead of tell.
While you may already be satisfied by my elaborate answer, I acknowledge your wish for concrete examples - and I am willing to show you the extend of my abilities to make sure you understand what I am trying to convey.
To answer you real question: there are lots of ways; some of which I will show you now.
Do you know what this answer is currently missing? Examples! Examples, examples, examples!
While there are lots of ways how you can express the same thought it is very difficult to imagine this by just reading boring excerpts from other sites and baseless assumptions. I will now show you how you may easily express different voices.
It's difficult to express yourself in a way that is not your own voice. But I will give it a try. I hope you are satisfied if I mention the same sentence a couple of times to express my thoughts.
The identical thought may be expressed in a great number of ways - some of which are easy to understand and some of which are not; some of which are easy to write for me and some of which are not; some of which may feel natural and some of which may not.
You urged me to give you examples - and examples I will give you!
To the best of my abilities I will test how to make my own writing as if it were not written by me.

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