Can I upload journal articles to a private git repo? I have some journal articles that are obviously copyrighted in some form that I am not allowed to share with people who don't have a license. 

I also have a private student git-repo. I want to know if it's okay to upload these articles to the repo, considering the repo is private?
I store all important papers in a cloud, where I am the only one (beside the operating people) that has access. There are several such cloud solutions around, such as from DropBox, Microsoft and many others.
Unless there is an explicit statement that does not allow this, it is perfect (and until now, there has not been such a statement). The key is that you restrict access to yourself.
I would not use git for your case; it is intended for software development.