Is omou transitive verb or intransitive? I learned that it's transitive from a dictionary but i can't see any "" before the word that's why I'm not completely convinced that it's transitive. Is it intransitive or is there exceptions?

Both. . . and. . . are common. But, contexts where occurs are much more frequent.

somethingmeans "(I'm) thinking of something" or "(I'm) thinking about something". Why is this one less frequent? Because it sounds a little bit more poetic thansomething, which is prosaic.

In contrast, the other form needs a clause: [clause], and means "(I) think that [clause]."

You sometimes see [noun], but this one is an irregular form and I personally avoid it in writing. The corresponding regular form is [noun]. For example, "Do you think we are enemies?" No. ---The more regular form is "I think (that) we are friends."