Oddly means in a strange or unexpected way. Something is not quite as it should be.
It works two ways in a sentence. Attached to a verb it describes behaviour, so behaving oddly means acting strangely. At the start of a sentence, with a comma, it flags the whole statement as surprising, which is where oddly enough comes from, and that phrase is one of the commonest in spoken English. Curiously and strangely do exactly the same job in exactly the same position.
Middle English
oddely
English, today
oddly
From Middle English oddely, odly, equivalent to odd + -ly.
Etymology from Wiktionary, CC BY-SA