Enable Auto Update Stats in Async mode We have a table with 10 billion records, where daily there are hundreds of thousands of updates/inserts/selects happening. As the auto-update stats was ON there were a few performance issues; hence, we turned it OFF and there were positive results.

Now, we want to turn the auto-update stats on in async mode, then perform another round of testing on it. How can the auto-update stats in async mode be enabled for one particular table?
You can't enable async auto-update stats for just one table. The setting is at the database level. 

I would recommend keeping auto-update stats enabled and also having an UPDATE STATISTICS job that runs on a schedule, perhaps daily. You could test doing a 10% sampling on the large tables rather than a more expensive fullscan.