I am making a few assumptions here so please bear with me. If you knew this already and it doesn't help, it could help someone else.
While items are in your inventory, you can drag them on top of each other, however the stack are created based on the type of item, and in the case of food, their quality. You cannot always have different types of quality food on top of another. This is dependant on which patch your running, some patches allowed it.
Once you have the stack correct, it will create a square in the top left corner of the stack, which you can grab and then drag onto the fridge. This should add all the items to the fridge.
Sadly, there is no way to stack everything you want into one big pile and then add them to the fridge. i.e. You can't mix fish and tomatoes, or even tomatoes and potatos together. The stacks of the same item and group drag is the closest you will get.