Would one sound like a native German speaker saying "nen" instead of "einen" or is there another special point behind it? Does it have colloquial usage only?
Yes to both questions. It's only used in colloquial speech by native speakers or when chatting online with friends.
The use of "nen" instead of "einen" is colloquial speech. It doesn't deliver any additional meaning, much like the abbreviation of "does not" to "doesn't". You should never use it in formal German, but especially in spoken language it is often used.
Attention: As pointed out in the comments to your question, "einen" is shortened to "'nen", but "eine" is shortened to "'ne" and "ein" to "'n" - you simply replace the "ei-" by an apostrophe.