Yup, some processes of brewing are not pretty!
Keep that beer in primary for 2-3 weeks to finish and begin clearing. You don't take the beer out of primary until you are sure it's done meaning no changes in gravity.
Then rack into not oak in secondary. The beer will continue to clear and take up the oak flavors. As long as FG was verified before racking there should be no further fermentation occurring in secondary and that's the way it should be