Did you look up 曰く in a dictionary? This 曰く is a noun meaning "story/tale/past/history". It refers to some shady background associated with something/someone. The phrase doesn't specify the exact nature of the history, leaving it open to interpretation based on the context. In particular, it does not necessarily imply it is haunted or cursed. For example, 曰く付きの男 ("a man with a past") may imply that he has something to do with the underworld society, but it does not usually mean he is possessed. In the context of that manga, it does seem likely that some sort of curse or possession is involved, but it is not explicitly stated as such.
いわく in this sense is pronounced like いわく【LHH】, whereas 曰く meaning "according to" is pronounced like いわく【HLL】. Etymologically, 曰く is 言う nominalized with something called ク語法, so its original meaning is just "saying".