There are so many options if no relationships are given that it is all speculation. Are they enumerated in random order or in order they movd in?
Elizabeth could be Jasper's mother, or aunt. Martha Lutes could be Jasper's daughter, but could also be Elizabeth's daughter (she'd have been 39, which is possible). Jasper, Willington and Nelson could all be Elizabeth's children, but they could also be Jasper's siblings (as, incidentally, could be Martha). Jasper (the younger) could be a cousing, while the rest are siblings. Added to that, not all of the Lutes in this list (excluding Elizabeth) need to be from the same mother. If the father of Jasper remarried after his mother died, he could've had half-siblings (one whom might have been named Jasper because of naming conventions that point to wife #2's family) that are still named Lutes.
All in all, with just one record and no more information, it's going to be impossible to try and determine how these people are related. Your best bet would be to try and find all of them in more than just this record and then combine that information to form a hypothesis. Or maybe more records will give you the answer you're looking for.