Here are the facts that we have from the canon:
1) Tom Riddle did not know that he had a muggle father and being sorted into Slytherin - I dont think either he or the fore-runners to death eaters had reason to suspect that he wasn't pure blood.
"Those whom I could persuade to talk told me that Riddle was obsessed with his parentage. This is understandable, of course; he had grown up in an orphanage and naturally wished to know how he came to be there. It seems he searched in vain for some trace of Tom Riddle senior on the shields in the trophy room, on the lists of prefects in the old school records, even in the books on wizarding history. Finally he was forced to accept that his father had never set foot in Hogwarts. I believe that it was then that he dropped the name for ever, assumed the identity of Lord Voldemort, and began his investigations into his previously mother's family - the woman whom, you will remember, he had thought could not be a witch if she had succumbed to the shameful human weakness of death."
-- Harry Potter and the Half Blood Prince - Chapter Seventeen: A Sluggish Memory.
I believe that both his reasons for dismissing that his parents were magical were faulted in both cases. In the case of his mother, the fact that she was unable to escape death was not reason enough to assume she was non-magical. And in the case of his father - lack of evidence that he attended Hogwarts (that too from the looks of his places of research - was among the best of students at Hogwarts) should not have been proof enough to conclude his father was non-magical. So - the fact that death eaters like Avery and Lestrange knew his name does not conclude that they knew he was a half-blood.
2) We know that Morfin was the one who revealed Voldemort's parentage to him
"I though you was that Muggle" whispered Morfin "You look mighty like that Muggle".
"What Muggle?" said Riddle sharply.
"That muggle what my sister took a fancy to, that Muggle what lives in the big house over the way," said Morfin, and he spat unexpectedy upon the floor between them. "You look right like him. Riddle. But he's older now, in 'he? He's older 'n you, now I think on it...."
-- Harry Potter and the Half Blood Prince - Chapter Seventeen: A Sluggish Memory.
From what Dumbledore says later on regarding Slughorn's real memory, we can say that Voldemort discovered that his father was a muggle when he was 15-17 years old. So he was nearly done with his schooling.
3)
"I don't know that politics would suit me sir" he said when the laughter died away. "I don't have the right kind of background, for one thing."
A couple of the boys around him smirked at each other. Harry was sure they were enjoying a private joke, undoubtedly about what they knew, or suspected, regarding their gang leader's famous ancestor.
"Nonsense," said Slughorn briskly, " couldn't be plainer you come from decent wizarding stock, ability like yours."
-- Harry Potter and the Half Blood Prince. Chapter Twenty Three - Horcruxes.
Going by the answer to Did the Death Eaters know that it was Voldemort who first opened the Chamber of Secrets? , it looks like some of the death eaters also knew that Voldemort was the Heir of Slytherin. Even without having that knowledge, Slughorn was able to accept that Voldemort was pureblood. So knowing that would have probably only increased Voldemort's blood status in the eyes of the Death Eaters.
4) Voldemort has always been very secretive.
"I trust that you also noticed that Tom Riddle was already highly self-sufficient, secretive and, and apparently, friendless? He did not want help or companionship on his trip to Diagon Alley. He preferred to operate alone. The adult Voldemort is the same. You will hear many of his Death Eaters claiming that they are in his confidence, that they alone are close to him. They are deluded."
-- Harry Potter and the Half-Blood Prince. Chapter Thirteen - The Secret Riddle.
That to me indicates that even though he had found and wiped out his entire muggle ancestry - he need not have told anybody about it. I suspect that Voldemort would have been eager to reveal details about his parentage when he had to work hard to find out for himself AND when the discovery was not very pleasant - to say the least. Again - the strong possibility that the Death Eaters figured out that he was the Heir of Slytherin, instead of him bragging about it, indicates that he wouldn't have shared the fact that his father was a muggle.
5) Voldemort refers to his muggle father twice - once in the Chamber of Secrets - where his memory reveals it to Harry. And again in the graveyard where he regained his body.
"You think I was going to use my filthy Muggle father's name forever? I, in whose veins runs the blood of Salazar Slytherin himself, through my mother's side? I, keep the name of a foul, common Muggle, who abandoned me even before I was born, just because he found out his wife was a witch? No, Harry - I fashioned myself a new name, a name I knew wizards everywhere would one day fear to speak, when I had become the greatest sorcerer in the world!"
-- Harry Potter and the Chamber of Secrets. Chapter Seventeen - The Heir of Slytherin.
In that instance - it was only Harry to whom Lord Voldemort was talking.
"You stand, Harry Potter, upon the remains of my late father," he hissed softly. "A muggle and a fool... very like your dear mother. But they both had their uses, did they not?"
-- Harry Potter and the Goblet of Fire. Chapter Thirty-Three - The Death Eaters.
In this instance - he was speaking to Harry Potter. But Wormtail was also nearby.
6) Apart from that - the only indication that we have that any death eater knew about Riddle's father was Barty Crouch Jr's statement - when he was still pretending to be Mad-Eye Moody.
The Dark Lord and I", said Moody, and he looked completely insane now, towering over Harry, leering down at him, "have much in common. Both of us, for instance, had very disappointing fathers... very disappointing indeed. Both of us suffered the indignity, Harry, of being named after those fathers. And both of us had the pleasure... the very great pleasure... of killing our fathers to ensure the continued rise of the Dark Order!".
-- Harry Potter and the Goblet of Fire. Chapter Thirty-Five - Veritaserum.
So from the books - I can conclude that only Wormtail and Barty Crouch Jr seem to have known that Voldemort was Half-Blood. Even Barty Crouch might have only suspected - not known that Tom Riddle Sr was a muggle.
