Your full brother's son's DNA would. Your son's DNA or your sister's son's DNA would not. Your paternal half-brother's son's DNA would. Your maternal half-brother's DNA would not.
Your son's DNA would help for finding his father's relatives, but would not help for finding any of your relatives whom you could not find with your own DNA. His Y DNA would not help at all for finding your relatives, because it comes only from his father. If your DNA was not available to test, then his regular DNA would help with finding your relatives, because half of it is from you, but it would help only to find relatives whom you would also find with your own DNA, and you are more likely to find them with your DNA than his, since he has only half of your regular DNA.
Similarly, your sisters' sons' DNA, would help for finding THEIR fathers' relatives, but their Y-DNA would not help you find YOUR father's relatives.
However, your brother's sons' DNA would help for finding your brother's father's relatives. If your brother is either your full brother (same father as you and same mother as your) or your paternal half-brother (same father, different mother), then these would be your paternal relatives. If your brother is your maternal half-brother (same mother, different father), then these would not be your relatives.
1) In the Torah, Abraham says that Sarah is his father's daughter or granddaughter (but not his mother's); therefore, Sarah could learn about the relatives of Terah (her father or grandfather) by testing the DNA of Isaac (her son and also the son of Terah's son Abraham), if DNA testing had been invented. However, it would be no more useful than testing the DNA of Ishmael (the son of Abraham and Hagar, another woman, whom we will assume is not related to Sarah). The same would apply today. Similarly, if a woman's father is also her sister's sons' father, then DNA testing them would be useful, but only as useful as if she was not related to their mother.
2) There are rare cases of a person being born anatomically female, but with a Y chromosome. The person appears to be a normal female (or even slightly less masculine than a typical woman) and often does not find out that they have a Y chromosome. If your son is adopted, then there is a remote chance that you might have Y DNA that could be tested. However, a person with this condition is not able to have biological children. (They don't have ovaries or a properly functioning uterus.) If you gave birth to your son (whether with your own eggs or donor eggs) or used a surrogate with your eggs, then you definitely don't have Y DNA. (Finally, a transgender person who was born male, but now self-identifies as female, would still have sufficient Y DNA to have it tested and would not need to use the DNA of a male relative.)