He asked me a question.

He asked a question of me.

He begged me a question.
He begged a question of me.

He inquired me a question.
He inquired me of a question.

(Are the pairs all correct and interchangable? Doe they have the same meaning?)

3 answers

The first pair is correct and interchangeable, but the others aren't.

The 3rd sentence is not correct.

The 5th and 6th are not correct. For this, you'd need to say, "He inquired about .... " (The "me" part wouldn't be there.)
3. He begged me a question.
4. He begged a question of me.

5. He inquired me a question.
6. He inquired a question of me.

(Thank you for your help. #6 should be changed. Among the four sentences, which ones are not grammatical? Is #6 correct?)
Among these four sentences, only #4 is correct. The word "inquire" is not used with an indirect object or "to" and an object.

He inquired about my illness.
He inquired about their children.
He inquired about the train fare from Washington to New York.