over vs o'er

over is a noun but o'er is not a noun.

Word	Noun	Adjective	Verb	Adverb
over	Yes	Yes	No	Yes
o'er	No	No	No	Yes

As adverbs, over and o'er are synonyms defined as:

over (noun)	o'er (noun)
(cricket) the division of play during which six balls are bowled at the batsman by one player from the other team from the same end of the pitch

over (adjective)	o'er (adjective)
having come or been brought to a conclusion

over (adverb)	o'er (adverb)
throughout a period of time	throughout a period of time
at or to a point across intervening space etc.
throughout an area
beyond the top or upper surface or edge; forward from an upright position
over the entire area