From Lime Odyssey Wiki
There are 2 modes of storage within Lime Odyssey, the Backpack and the Warehouse.
You start out in Lime Odyssey with a backpack that can hold 30 items. This is fine for a starter but as you progress you may find yourself wanting more space to haul home the loot in. You can upgrade this by purchasing more backpacks from the in game cash shop. You may add up to 4 other upgrade bags, and each upgrade bag holds an additional 20 items. This means you have an impressive total of 80 possible item spots!
When you start the game 2 of the "upgrade" bags are enabled but will only last for a limited amount of days (I believe it is 10). Once they are disabled you will not be able to put items in them but the items already in them will be able to be removed from them. When you go to sell an item in a "disabled" backpack, it will not sell. You will need to remove the item(s) from the disabled backpack to the enabled one.
You don't need to carry all your items with you everywhere you go, and you are better off saving that space for some fancy rewards on your travels. You can visit a Warehouse Keeper in any major city to open a bank where you can keep the items you don't need right away, but don't want to sell.
It costs 100 Silver to open your warehouse upfront, and after that you can pay to increase your warehouse size - but it gets increasingly expensive, up to 16 gold. If you speak with a Warehouse Keeper they will show you the cost of every warehouse expansion.