What are some good and authoritative references/data sources for modern usage examples of words? My typical workflow of learning a new word is to look it up on OED and read the definitions and example sentences. But a huge drawback and uncomfortableness is that OED's example sentences are typically old or oldest usage example sentences that their editors could find which is NOT the best resource for learning the words' usage in modern context. What are some other references and data sources I should use to complement OED?
I'd say that if you've got access to the full OED then that's a good place to start. No other source has (nor probably ever will have) that level of acknowledged expertise (as opposed to unaccredited sources like Urban Dictionary, or those like TheFreeDictionary that effectively "scrape" other dictionaries).
If you want to get a better handle on how the way a word is used might have shifted in very recent times, you need to bear in mind that some usages which might appear ubiquitous today may very well turn out to sound extremely dated (or even be unfamiliar to most) within a very few decades. I don't know, but my guess is most new usages don't actually last long (doubtless that's part of the reason dictionary editors tend to be conservative! :)
What I think you are looking for is a number of examples of a target word in a sentence or paragraph (most dictionaries will give at least one sentence in its definition).
The OED is great (arguably the best) for definitions of words, with nuance provided by finely differentiated subdefinitions. Also, a number of context sentences are given to show it's historical usage (the first known appearance and then a handful of later appearances). Unfortunately these citations don't always give the full context.
A corpus, a well-curated collection of texts, should give not only good coverage of vocabulary in narrative texts, but also allow for you to search for individual items and look at the original text, the surrounding sentences for fuller context.
The most easily available corpora are:
But see the longer list of corpora here.
Because these are curated, they are likely to have few errors, but are more likely to come from formal sources (newspapers, official transcripts).
Internet search engines, like Google, give copious examples of search terms in context. However, the entire world is not curated, and the examples are not necessarily formatted well or even sentences. But it might be the easiest and quickest to use.