Enriching uranium creates depleted uranium. They are two sides of the same process. Depleted uranium is natural uranium that has had some U-235 removed from it, and enriched uranium is natural uranium which has had some U-235 added to it. This is where depleted uranium rounds come from. The irradiated spent fuel which SR was talking about does have a lot of U-238, but also a lot of undesirable and highly radioactive contaminants, so it cannot be "efficiently recycled" into DU ammunition. It would be possible to do so in theory, but it would be costly and more technically challenging than obtaining DU from natural uranium. It would also be contaminated with some U-236, which would make it very obvious where it came from.
Likewise for making nuclear bombs from spent fuel. The amount of U-235 remaining in spent fuel is small, and it too would be contaminated with U-236, so again, natural uranium would be a far better source of U-235. Spent fuel also contains some Pu-239, but it too is heavily contaminated (with Pu-240), which makes it worthless for bombs. Out of the tens of thousands of nuclear bombs which have ever been made, zero have been made from spent fuel. The Brits tried to make an experimental bomb from reactor fuel by pulling it of their Magnox reactors early, long before it could actually become spent, and it did produce an explosion, but the cost involved and the poor performance of the device convinced them the standard approach of toasting U-238 in bomb-making reactors which were purpose built for that task was the far superior route.
So the question remains, what sort of weapons can be made efficiently from spent fuel? Or failing that, what weapons have ever been made from spent fuel?