Magento 1.9 – How to Get Order Id from Item Id

All you need to do is, invoice and ship only the item that the customer needs. Once that is done, you need to cancel the order. It will turn the order status to complete and mentioning the other items are cancelled. Please check the attached

There is no direct way to load Order Object using Order Item Id.

But if you Load Order Item Object using Item Id then you can directly get the Order Object using function getOrder

you can check this getOrder function in Magento\Sales\Model\Order\Item class.