Your two statements are contradictory. In your first, you say that your opinion is "there's no difference". In the second, you said you feel "there's a subtle difference". Which one is your actual opinion?
I was looking at his eyes = I might be looking at a photograph of his eyes, or he may have two glass eyes and has put them on the table and I am staring at them.
I was looking into his eyes = We were looking at each other, both staring into the other person's eyes.
I was looking at him = My vision/sight was directed at him. It is not clear where he was looking.
I was looking into him = I was investigating him (perhaps a criminal matter).