Is it possible to have a status field(say an option set - Fulfilled and Out of Stock) for each item in the order product inline editable grid? I tried adding a field "Item Status" to the Order Line entity form and editing the view but it does not work. Using a third party solution is not an option.
It's not possible to change the out-of-the-box editable grids. Custom editable grids were introduced in Dynamics 365, but still you will not be able to use it for this case, because they do not support Order Products. You would have to create a custom Order Products if you want to use it, but I believe that's not what you are after. So third-party solution is the only option.