I really like this game. I'm just wondering whether there is an NTR route cuz some characters such as oliver hint at it
Some decisions can lead to the ladies not being interested in you. As long as the path is active, the girls will not be interested in other guys. Strictly speaking, the mother and the teacher (she has a fiancé) would fall into the category of NTR. But as I said, there will be no case where most of the ladies (except for the teacher, where we don't know what she does when she's not around) will show interest in other guys as long as the path is active.
And as for Oliver, he can definitely try. Whether he succeeds is another story.