As for the vedas, specifically Rigveda (which is the only one I can comment on with some expertise) we have what we can call different recensions of the text. These texts, independently transmitted, differ very little from each other. This fact alone strongly indicate that even while they've been orally transmitted for many generations, they are more or less uncorrupted by the act of transmission.
Much more could be written on this subject (and has been). However, english isn't my native language, it is late and this comment could go on and on…short story is: memorization and oral transmission seems to work!
This is important. This constraint alone helps oral traditions a great deal.
Imagine you had to pass down a Java program (through oral tradition) to sort numbers and you had a Java Language Specification that remains unchanged. Now compare that to say English language where and you write an essay on sorting numbers. If both things are passed down orally over few dozen generations which one is likely to keep its form ?
What this meant was that language stopped evolving since last 2400 years ago. You can create new words but there are precise rules for it. All this means there is no scope for "dialects", words meanings changing with geography etc. Different vedic chants separated by thousands of miles and 1000 years in time are exactly the same and perfectly understandable in any part of the country for anyone who has studied Sanskrit.
This makes Vedic chants unlike anything English, Latin or Arabic has to offer.