Think about the physical interpretations of the prepositions. "Into" means "in to". It is directed at the core of its object. "Over" means above. It stays away from the core of its subject. If I go into a house I will be inside. If I go over a house I will be on the roof or in the sky. So "look into" means investigate or examine. "Look over" means the same but in a less serious way.

To me "to investigate" is to search for something, and "to examine" means to evaluate something, to decide whether it is good or not, or to decide whether it meets some criteria.