How to frame sentences using the following 'says', 'believes', 'is of the opinion'?can u give some examples?

In conversation: He says the President is right.
Grammatically correct: He says that the President is right.
In that example, it means believes and is of the opinion. Says can also just be a statement of fact: 'He says he went to the store an hour ago.'
Believes is much closer to 'is of the opinion,' USUALLY.
He believes (that) the President is right.
But sometimes people say believe when they mean they plan to do something that they might not have planned to do, or that people wouldn't expect them to do, and it has nothing to do with opinion. 'I do believe (that) I will actually clean out the garage today.' But that would be speaking in the first person, almost always. It has a hint of opinion to it, because the speaker might not really follow through.
'He is of the opinion that the President is right' is very much like believes, and probably seen more in writing than in casual conversation. And 'that' would not be left out.