Here's what the different house statuses mean in Tibia:
Rented
The house currently has an owner. It's occupied and unavailable until the owner sells it, moves out, loses premium, or can't pay the rent.
Auctioned
The house is empty and available through the house auction system.
If no one has bid yet, it still shows as auctioned. Once someone places the first bid, the auction actually starts and the status updates with the current bid and time left.
Scheduled for renovation
The house is temporarily locked and can't be rented or auctioned.
This happens during world merges. When a merge is announced, all house auctions on the affected worlds are cancelled and no new ones can start. Current owners keep their houses until shortly before the merge. (Source)
Unrentable
This one is rare and not officially explained. The house is empty but doesn't go through the normal auction process and can't be rented. From what people have reported, it seems to be some kind of internal/admin state, possibly after manual intervention by CipSoft (for example when a house was taken and later given back). (Source)