The recyclers where I’ve lived lately won’t accept them. This is why boxed oil is less wasteful. Less plastic used and the cardboard gets recycled.
If the Havoline Box cardboard is not fully drained and has even a small amount of oil in it, it won't get recycled.
L / XL Cardboard Pizza boxes that have food remnants on the box-bottom, won't get recycled either.
Large plastic Can't Believe It's Not Butter tubs that have butter-remnants inside, won't get recycled. Rinse them out first. Mayo, Ketchup and mustard containers too.