I am not sure of the answers to your specific questions. Certainly eggnog could be canned professionally, but home canned? I am not sure how good the process is, because I don’t have a lot of knowledge about it, hopefully someone else will know. I would assume you can, that the processes goal is a sterile canning that is airtight? Again, I am not knowledgeable really.
I don’t know what an egg casserole is. But, generally I say back first then freeze about casseroles.
I do have suggesstions though. Cakes freeze very well, if you want to make several of those. You can just make the layers, you don’t have to do all the icing. When you need a cake you can defrost whichever flavors you want in the cake and put the layers together. You can bring cakes to parties/social get togethers, and eat them in your own home. Of course you can make other types, pound cakes, coffee rings, whatever you choose.
You can make pasta, bake some pasta dishes like lasagna, freeze them, and use them for dinners over the next few months.
Also, maybe you can give them away or trade with friends and neighbors. Some people might have extra tomatoes in their garden.