I do wish someone on this board had access to a lab for rancidity testing.
Nut oils are fragile, but polyunsaturated oils are well known to last longer in whole nuts/grains than if ground, sliced, or diced. My experience is that nuts do considerably better stored with oxygen absorbers than with just vacuum canning, but I've never seen anything on nuts in their shells canned that way. It would be nice to see some solid lab numbers on that, since they do keep better unshelled than shelled when raw (25% to 50% longer on average). It would also be interesting to see how getting them out of contact with all oxygen after shelling works versus intact nuts in their shell in a zero-oxygen environment. All the available data is based on either vacuum-sealed in plastic whole nuts or nitrogen-flushed shelled nuts in cans/jars.
Ideal storage for most nuts is supposed to be 0 to 10 C at 50% to 70% humidity, so I expect the fact the OP had his refrigerated for half the storage time and in a cool house the rest had a lot to do with his satisfaction when he opened the cans. He's going to get noticeably less shelf life with them stuck under the house where it gets to 80 degrees in the summer.
My recommendation would be to package with O2 absorbers and freeze. If using shelled nuts to save space, also apply some rosemary-tocopherol-ascorbic acid antioxidant before packaging. Almonds will last noticeably better than walnuts, but even walnuts and pecans should have at least a 2- to 3-year shelf life frozen in zero oxygen, and unshelled almonds should still be good for a year or two after defrosting if you stick to a 2-year rotation in the freezer.
While I agree with Zeke that the ideal solution is to plant a bunch of nut trees on your property, I am one of many for whom that advice isn't of much use. So it would be really nice to see some hard numbers on how the oils in various nuts and oil seeds fare in different storage conditions in a zero-oxygen environment.
ETA: Blue Diamond gives its raw almonds in the shell stored in ambient conditions in plastic bags a 36-month shelf life, so the OP may be quite right that those were fine after 5 years stored in cans in a zero-oxygen atmosphere. I would doubt his wife's nose if she thinks the walnuts are equally good, but she may be quite right about the almonds.
http://www.bdingredients.com/food-safety/
Unfortunately, their only canned products have been sliced/diced/chopped and/or blanched or roasted, all of which things greatly decrease shelf life, so no numbers for unshelled almonds packaged with oxygen absorbers.
ETA:*Rainy Day/Walton gives its shelled pasteurized raw almonds in #2.5 cans up to a 3-year shelf life stored at 60 degrees or less, but I have no information on what they base that on. Blue Diamond gives its whole natural pasteurized shelled almonds in nitrogen-flushed cans a 2-year shelf life for normal pantry storage (which they have to assume is going to be more like 70 degrees or above) on the linked chart, but the cans I have here have a best-by date 3 years post manufacture. I count my shelled almonds packaged with oxygen absorbers and antioxidant and frozen as good for 3 years in the freezer and another year on the shelf or 2 years in the freezer and another 2 on the shelf although I have no Rancimat numbers to prove it. In the shell, I would think that you ought to get up to 3 years in the freezer and another 2 on the shelf. (I don't have enough freezer space to freeze in-shell nuts, though.) Walnuts or pecans would have shorter storage lives. Planters dates its walnuts in nitrogen-flushed canisters for 1 year. I can't remember what Diamond gives its similarly-package walnuts with added BHT, but it may be as much as 18 months. Of note, there is research showing that most of the rancidity in walnuts is oxidative, so storing with an oxygen absorber should give much better results than vacuum packaging and somewhat better results than nitrogen flush as well.
http://pubs.acs.org/doi/abs/10.1021/jf60030a006?journalCode=jafcau
If packaged with an oxygen absorber and natural antioxidant, you should be able to store your walnuts and pecans frozen for a couple of years or frozen for a year plus a 6-month to 1-year pantry shelf life depending on temps. I would devote more of your freezer space to longer-lived nuts like almonds, though. (Note, sunflower seeds have a 1-year storage life in ambient conditions, so are intermediate between almonds and pecans or walnuts.) I really wish some of the oxygen absorber manufacturers would sponsor some rancidity studies on various varieties of nuts packaged with them rather than nitrogen flush. Given that most of the rancidity in nut oils is oxidative, there should be a real difference between storage in 2% to 3% oxygen and storage in less than 0.01% oxygen.
I agree that nuts are not long-term storage candidates other than growing them on trees, but there are ways to get them into mid-term storage on a shortish rotation. As with oils, the way to do that is to use a freezer up until the lights go out. With oils, you can also add some antioxidants to cold-pressed oils and nitrogen-flush the jars or cans for max shelf life. With nuts, you add some antioxidants and package in mylar or jars with O2 absorbers. You should be able to store a couple of years of nuts used on a regular rotation or your current harvest plus a year's backup supply off your trees. (Since nut trees don't necessarily give you a nice harvest every year, especially if you don't have an orchard-full of the things, getting a couple-of-year storage life is of interest to even most of those who have trees.)
Nut oils are fragile, but polyunsaturated oils are well known to last longer in whole nuts/grains than if ground, sliced, or diced. My experience is that nuts do considerably better stored with oxygen absorbers than with just vacuum canning, but I've never seen anything on nuts in their shells canned that way. It would be nice to see some solid lab numbers on that, since they do keep better unshelled than shelled when raw (25% to 50% longer on average). It would also be interesting to see how getting them out of contact with all oxygen after shelling works versus intact nuts in their shell in a zero-oxygen environment. All the available data is based on either vacuum-sealed in plastic whole nuts or nitrogen-flushed shelled nuts in cans/jars.
Ideal storage for most nuts is supposed to be 0 to 10 C at 50% to 70% humidity, so I expect the fact the OP had his refrigerated for half the storage time and in a cool house the rest had a lot to do with his satisfaction when he opened the cans. He's going to get noticeably less shelf life with them stuck under the house where it gets to 80 degrees in the summer.
My recommendation would be to package with O2 absorbers and freeze. If using shelled nuts to save space, also apply some rosemary-tocopherol-ascorbic acid antioxidant before packaging. Almonds will last noticeably better than walnuts, but even walnuts and pecans should have at least a 2- to 3-year shelf life frozen in zero oxygen, and unshelled almonds should still be good for a year or two after defrosting if you stick to a 2-year rotation in the freezer.
While I agree with Zeke that the ideal solution is to plant a bunch of nut trees on your property, I am one of many for whom that advice isn't of much use. So it would be really nice to see some hard numbers on how the oils in various nuts and oil seeds fare in different storage conditions in a zero-oxygen environment.
ETA: Blue Diamond gives its raw almonds in the shell stored in ambient conditions in plastic bags a 36-month shelf life, so the OP may be quite right that those were fine after 5 years stored in cans in a zero-oxygen atmosphere. I would doubt his wife's nose if she thinks the walnuts are equally good, but she may be quite right about the almonds.
http://www.bdingredients.com/food-safety/
Unfortunately, their only canned products have been sliced/diced/chopped and/or blanched or roasted, all of which things greatly decrease shelf life, so no numbers for unshelled almonds packaged with oxygen absorbers.
ETA:*Rainy Day/Walton gives its shelled pasteurized raw almonds in #2.5 cans up to a 3-year shelf life stored at 60 degrees or less, but I have no information on what they base that on. Blue Diamond gives its whole natural pasteurized shelled almonds in nitrogen-flushed cans a 2-year shelf life for normal pantry storage (which they have to assume is going to be more like 70 degrees or above) on the linked chart, but the cans I have here have a best-by date 3 years post manufacture. I count my shelled almonds packaged with oxygen absorbers and antioxidant and frozen as good for 3 years in the freezer and another year on the shelf or 2 years in the freezer and another 2 on the shelf although I have no Rancimat numbers to prove it. In the shell, I would think that you ought to get up to 3 years in the freezer and another 2 on the shelf. (I don't have enough freezer space to freeze in-shell nuts, though.) Walnuts or pecans would have shorter storage lives. Planters dates its walnuts in nitrogen-flushed canisters for 1 year. I can't remember what Diamond gives its similarly-package walnuts with added BHT, but it may be as much as 18 months. Of note, there is research showing that most of the rancidity in walnuts is oxidative, so storing with an oxygen absorber should give much better results than vacuum packaging and somewhat better results than nitrogen flush as well.
http://pubs.acs.org/doi/abs/10.1021/jf60030a006?journalCode=jafcau
If packaged with an oxygen absorber and natural antioxidant, you should be able to store your walnuts and pecans frozen for a couple of years or frozen for a year plus a 6-month to 1-year pantry shelf life depending on temps. I would devote more of your freezer space to longer-lived nuts like almonds, though. (Note, sunflower seeds have a 1-year storage life in ambient conditions, so are intermediate between almonds and pecans or walnuts.) I really wish some of the oxygen absorber manufacturers would sponsor some rancidity studies on various varieties of nuts packaged with them rather than nitrogen flush. Given that most of the rancidity in nut oils is oxidative, there should be a real difference between storage in 2% to 3% oxygen and storage in less than 0.01% oxygen.
I agree that nuts are not long-term storage candidates other than growing them on trees, but there are ways to get them into mid-term storage on a shortish rotation. As with oils, the way to do that is to use a freezer up until the lights go out. With oils, you can also add some antioxidants to cold-pressed oils and nitrogen-flush the jars or cans for max shelf life. With nuts, you add some antioxidants and package in mylar or jars with O2 absorbers. You should be able to store a couple of years of nuts used on a regular rotation or your current harvest plus a year's backup supply off your trees. (Since nut trees don't necessarily give you a nice harvest every year, especially if you don't have an orchard-full of the things, getting a couple-of-year storage life is of interest to even most of those who have trees.)