"refurbish" and "renovate" are close in meaning, but "renovate" to me suggests more of changes in structure whereas "refurbish" could just be furnitute. "restore" would be used if you brought the house back to its original condition. Let's say the house was abandoned and neglected. If you restored it, then the house would be just like it was when it was first built. "repair" is similar to "restore" but isn't necessarily as drastic.
I'd say that the difference between repair and restoration is that restoration has, as its objective, returning the house to the way it was when it was built. (There are obviously practical considerations here. Someone restoring an 18th-century home would probably want electricity, indoor plumbing, and in my climate central heating.) Repair is fixing what is broken so it works properly and looks good, but it doesn't necessarily look like the original. Someone repairing an 18th-century home, if he or she was not concerned with appearance, might use 21st-century exterior materials, single-pane insulated windows and so on.