I use corks to fit in the ports, nice fit, mouse-proof, easy to remove, and can be found in any hardware store cheap...sometimes I can find them made of rubber, those are nice too.
I have also tried to cover the engine during the winter, the mice like to get under the cover and raise families...didn't like that, also found that in temperature fluctuation condensation and oxidation occurs faster because it takes longer to dry off.
I 've been keeping my "ready " engines on a large baking sheet, indoors, with the oil pans off so they sit sturdy, all other related pieces to each engine on same pan. Along with the ports being corked and on a shelf well from the floor.... those engines have engine building lube in them and haven't been run yet. No place for mice to hide , and is open to the air should it need to have condensation evaporate...so far no mice ,looks dry , no visible oxidation, and still looking new. they are in the unheated barn, my goal is to move them to a heated space cause I'll feel better about it.
The spare "not rebuilt" engines don't get that treatment. They are intact, with blocks underneath them that keep them in the upright position. the ones that spin gets corks only. The ones that don't spin ... well, what's the difference as long as they are clean and dry, they are already screwed,and definitely in better circumstances now then when they were found. They are on a shelf too.
Lifting is always an issue, so the "ready" engines are at waist height, as are next in line for rebuild. The stuck engines are near the floor with the junkyard found lower cases (in case I need tranny parts) . The top ends are on open air shelves.
Short of that, I think the next best thing, would be to set them in a barrel of oil and bury them in the constant 50 degree ground...but that sounds excessive.