When you move out of a house, choose the Sell Furniture option especially if you're moving to a house that's already furnihsed -- go through and make sure you have all your career reward items unless you don't mind buying them again, put those items in the household inventory then move and sell the furniture.
For selling harvestables, you can drag it from the household inventory over to the Sell area to the left as a group -- you can then choose how many you want to sell. (You get a plus/minus box so you can choose and see how much money you'll make.) If you want to put things in a box you have to drag them out into the world, then you can drag things into the box during Live Mode.
