I mean it's stupid right? He even
controlled possessed him in the 5th book briefly. He would surely realize that the sensation or whatever he felt and did while controlling Nagini was the same.
It was not the same. Harry is not a Horcrux. For my own explanation of it, look here, although if it's unclear I can restate it here. The controlling of Nagini and Harry were different things (in fact, he didn't control Harry, he just influenced him.) His soul can comment
To answer your question though, there are two possibilities. One is that Voldy did realize but didn't think he could do anything about it. Even if he figured that Harry contained a piece of his soul,he wouldn't think he could do anything about this. Remember that Harry survived because Voldemort took his blood to resurrect, not necessarily because of the piece of his soul (Voldemort actually killed his own soul, and would've killed Harry). Maybe he knew, and assumed that he could kill Harry and the piece of his soul--a worthy sacrifice.
However, that is unlikely. He knew that there was not much of his soul left after Harry's horcrux-hunting, so he probably would not reduce himself to simply one-quarter-soul (himself and Nagini) willingly. So what did he think about Harry? Well, it took Dumbledore's shrewd ideas to figure out the truth; Voldy probably thought something like what he told Harry:
“I miscalculated, my friends, I admit it. My curse was deflected by the woman’s foolish sacrifice, and it rebounded upon myself. Aaah . . . pain beyond pain, my friends; nothing could have prepared me for it.I was ripped from my body, I was less than spirit, less than the meanest ghost . . . but still, I was alive. What I was, even I do not know.
Snape sheds some light on the situation for us in book 5:
“It appears that the Dark Lord has been unaware of the connection between you and himself until very recently. Up till now it seems that you have been experiencing his emotions and sharing his thoughts without his being any the wiser. However, the vision you had shortly before Christmas —”
“The one with the snake and Mr. Weasley?”
“Do not interrupt me, Potter,” said Snape in a dangerous voice. “As I was saying . . . the vision you had shortly before Christmas represented such a powerful incursion upon the Dark Lord’s thoughts —”
“I saw inside the snake’s head, not his!”
It seems that he realized there was something here, and since Harry saw the snake's head, he knew it was something with his soul. Who knew how much he suspected. Dumbeldore also says:
“More recently,” said Dumbledore, “I became concerned that Voldemort might realize that this connection between you exists. Sure enough, there came a time when you entered so far into his mind and thoughts that he sensed your presence
Remember also that Dumbledore didn't realize that Harry would survive until he did, so Voldemort, even if he knew that Harry was a semi-Horcruxoid, might just kill him to get rid of Harry, since that, to him, would preserve his immortality.
Voldemort was an exceptionally skilled wizard, but he lacked the wisdom to understand all the consequences of the magic he performed, or even to recognize his failure to understand. Overconfidence is a common failing amongst the exceptionally skilled, and it is clear that Voldemort suffered from this particular failing in spades.
In particular, he took it for granted that he would be aware of anything that happened to his soul:
But surely if the boy had destroyed any of his Horcruxes, he, Lord Voldemort, would have known, would have felt it? He, the greatest wizard of them all, he, the most powerful, how could Lord Voldemort not have known, if he, himself, most important and precious, had been attacked, mutilated?
Deathly Hallows, chapter 26, abridged
Secrets of the Darkest Art, which Voldemort found in the restricted section of the Hogwart's library, warned that making a Horcrux would make your soul unstable, but Voldemort nevertheless believed that he was powerful enough to safely make not just one, but six Horcruxes. It simply never occurred to him that his soul might become unstable enough that a part of it could become unintentionally separated, without his even realizing it, even under extreme circumstances such as the backfiring spell that first killed him. In short, he was too arrogant to even consider the possibility.
It is also very likely, given his obsessive fear of death, that he was never willing to think very hard or able to think very dispassionately about the events of that day, or to carefully consider all of the possible consequences. Had he been able to do so things might have turned out differently.
As for the similarities between Harry and Nagini, I don't think the comparison is apt. Voldemort's control of Nagini was primarily based on his Parseltongue abilities. Making her into a Horcrux enhanced the bond between them (for example, that is probably why he could see through her eyes) but so far as we are aware he never attempted to use his bond with Harry in the same way. There are also other differences between the two; for example, Harry has a soul of his own whereas Nagini presumably doesn't, and Nagini was created intentionally (a process which presumably included all the usual protective spells applied to a Horcrux, or at least those which could be applied to a living thing) whereas Harry was an accident. More discussion.
It is of course possible (though hardly certain) that the sensation of sending false images into Harry's mind was somewhat similar to the sensation of seeing through Nagini's eyes. Even if this is so, it is likely that Voldemort would shy away from considering the significance of this. And, of course, he was concentrating on something else; it can't be easy to lie convincingly with your mind.
You also mention the incident in Order of the Phoenix where Voldemort briefly possesses Harry:
Then Harry's scar burst open and he knew he was dead: it was pain beyond imagining, pain beyond endurance -
And when the creature spoke, it used Harry's mouth, so that in his agony he felt his jaw move ...
Order of the Phoenix, chapter 36, abridged
It was never made clear exactly what sort of magic Voldemort was using to do this, but he would not have made the attempt had he not expected it to work, so it seems unlikely that it was at all related to the missing soul-fragment.
Admittedly, it does seem reasonable to expect that while possessing Harry he should be able to notice the presence of that soul-fragment, but you have to take into consideration that:
Voldemort only possessed Harry for a brief period;
It was extremely painful to do so, due to the conflict between his soul and Harry's, a conflict Harry won, due, according to Dumbledore, to Harry's ability to love;
And Voldemort needed to concentrate on Dumbledore, lest he attempt another attack despite the risk to Harry.
Between Voldemort's fear of Dumbledore and the pain of the conflict between his soul and Harry's, it is hardly surprising that he did not notice the soul-fragment on that occasion.
So, to sum up: Voldemort had an unrealistic confidence in the inviolability of his own soul, was both too arrogant and too afraid to even consider the possibility that this confidence may have been ill-founded, and was never given a particularly good opportunity to notice any evidence there may have been to suggest that it was. His failure to recognize this was certainly unwise, but was not at all unusual under the circumstances.
I personally wouldn't use the word "stupid". At least, not to his face.
As an aside, writing this answer brought to mind the alternative-universe fan-fiction Harry Potter and the Methods of Rationality, which lampshades several of the ... less likely ... aspects of the Harry Potter series as well as introducing some of the concepts I used above to explain why Voldemort might easily fail to see things that from an outsider's viewpoint might seem as if they should have been obvious. I can't recommend it wholeheartedly; it is somewhat too dark for my tastes, and can be unreasonably critical of the original's fantasy-world mindset. But it is generally well-written, and alternately funny and fascinating, and you may find it of interest.
You might also like the Evil Overlord List at TV Tropes, if you haven't seen it before.
Obligatory Warning: "Give a man a fact, and you interest him for a day. Give him a link to TV Tropes, and he'll be out of your hair for months."
He never fully understood the connection.
In an interview, J.K. Rowling says the Dark Lord didn’t fully understand the connection between his and Harry’s minds, and didn’t realize that Harry had a piece of his soul. He didn’t understand what the connection between their minds mean, so wasn’t able to use that information to realize Harry had a piece of his soul.
Maura: How come voldemort was no longer employing occlumency against harry, as he was in the 6th book
J.K. Rowling: He is losing control, and unable to prevent Harry seeing into his mind. The connection between them is never fully understood by Voldemort, who does not know that Harry is a Horcrux.
- Bloomsbury Live Chat (July 30, 2007)
As for him possessing Harry, he had possessed several beings that his soul was in no way connected to before he returned to a body.
“Only one power remained to me. I could possess the bodies of others. But I dared not go where other humans were plentiful, for I knew that the Aurors were still abroad and searching for me. I sometimes inhabited animals – snakes, of course, being my preference – but I was little better off inside them than as pure spirit, for their bodies were ill-adapted to perform magic … and my possession of them shortened their lives; none of them lasted long …”
- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)
Though he doesn’t possess anyone other than Harry after he returns to a body, he may have been capable of it, and not thought there was anything unusual about his ability to possess Harry.
It is covered quite extensively in book 7 that Voldemort had no awareness when any of his Horcruxes were destroyed. Voldemort was aware of the connection to Harry but not why, and attributed it to the blood bond created when he returned to bodily form at the end of book 4.
Voldemort didn't know the ring, locket or cup had been destroyed. He knew about the diary only from Malfoy. Voldemort himself assumed he'd know if a horcrux was destroyed but he was wrong.