More than one tree/trees release/releases oxygen even at night.
Can anyone explain me which options are correct in both the cases?
Well, I wasn't sure about your question but I've found this very useful entry in the Oxford Dictionaries Blog where your case is specifically explained.
Let me quote an excerpt:
(1) More than one in five Britons are now classed as obese.
Phrases such as more than one in five /ten etc. can cause problems because people may think the subject is singular. In fact, the subject is plural (Britons, not one Briton) so you should use the plural verb are.
However, if you use the phrase more than one with a singular noun, then the verb should also be singular, even though the underlying meaning is plural:
(2) More than one bathroom in the home is definitely an asset.
So if we apply what has been exposed above to your case, that matches the second example, it should be
More than one tree releases oxygen even at night.