In "Hamlet" is there any poetic justice in the manner which Claudius, Gertrude, and Laertes die?
Yes, there is. They all die as a result of their own conniving and scheming to take Hamlet down. The plan was only for Hamlet to die, not for anyone else to. Claudius and Laertes were the ones to come up with the plan; they were the ones to put poison on the blade and in the drinks. It was they alone that set up the circumstances that, in the end, lead to their own deaths. That is poetic justice right there. As for Gertrude, she was an innocent bystander and didn't have a direct hand in the conniving, and ends up being a victim to her new husband's schemes to kill her son. Claudius never meant to have Gertrude die, but couldn't stop her from drinking, for fear of revealing his own devious plans. If he would have jumped in and said, "Hey! Don't drink that honey! That drink is poisoned--meant for Hamlet," he would have exposed himself as the murderer that he truly was. So, he had to sit by, watch his wife drink the poisoned wine, and pretend that he was surprised by it, in order to cover his own tracks.
If the king and Laertes had just left things alone, and had the duel without all of the poison and plotting, then they could have come up with a different way to get rid of Hamlet, one that hopefully didn't lead to their own deaths. But, they threw the poison in, thinking that owuld gurantee Hamlet's demise. Little did they know that it would gurantee their own deaths as well. Poetic justice was served when their own evil plots of revenge turned against them, taking them down as well. This could be considered a profound statement by Shakespeare about the destructive influence of hatred and revenge. I hope that those thoughts helped; good luck!