Have recently read The German War: A Nation Under Arms, 1939-1945 by Nicholas Stargardt and Japan at War: An Oral History by Haruko and Theodore Cook and really enjoyed getting a more personal and Axis-oriented perspective on the conflict. For the sake of completion, I'd like to read some similar works on some of the minor Axis (or I guess Axis inclined) powers like Italy and/or Finland.
Any suggestions would be appreciated!
I presume you can't read Finnish?
Because in that case your options are frankly rather limited. Gordon Sanders's "The Hundred Day Winter War" intersperses the battle narrative with accounts from the home front. It's a good read, but unfortunately I don't know of any non-fiction works in English that focus on the home front or even deal with it in detail.
Of fiction, the only one I know that has been translated is Väinö Linna's "Under the North Star" trilogy, which examines Finland's history from 1890s to 1950s from the viewpoint of inhabitants of a small village in Southern Finland. The third part deals with the 1930s and the war years, but it may be rather hard to grasp unless you first read the preceding two books.