I have a massively downvoted question with no answers and 2 votes to close. Does closing or deleting both refund my reputations lost? Or is it only deleting?
No, closing a question has no effect on your reputation, regardless of whether it is closed by you, by others, or by a moderator. Only deletion refunds lost reputation, and it refunds it regardless of who deleted it or why.
Things to note:
You do not regain reputation from voting to close the question, or having it closed, on their own.
However, once a question is closed, it becomes possible for users with high reputation to begin voting to delete it, which means that even if you can't delete it because there is an upvoted answer or multiple answers, those high-rep users can still vote to delete it, and if there are enough votes, it will be deleted, refunding the reputation.
Keep in mind, however, that the question will count negatively toward you in terms of post bans, as well as put a dent in your overall question record (questions that are downvoted, closed, and deleted count three times against you).