These are examples of idiomatic language. There is no rule guiding idiomatic use; people use it because they've heard it in their region, their home, their peer group. How it starts, I can only guess. Somewhere along the line, someone thought the extra word helped the verb to express more clearly what they wanted to express.
Use of idiomatic language can also indicate belonging. The classes can be: educated, race, area, ethnicity, beliefs, etc.
Chop the onions is a complete sentence. Up is an unnecessary addition. It does not impart a different meaning.
I was very stressed... Again, complete. Stressed out is popular among the young and is a kind of idiomatic expression. It may indicate to some an emphatic element. But in my experience, it's likely that the person saying stressed out is either young or spends a lot of time in the company of the young.
This is a good question for linguistic anthropologists - those who study the role of languages in the social lives of individuals and communities.