I noticed there is a solution to some of the items that can't be picked up. I'm reporting it in the hopes it gives some indication as to what is wrong with them.
Ammo - if loose (unboxed) ammo can't be picked up, it can usually be "split" which causes half the ammo to end up in your inventory (provided there is space)
Weapon - if space is available on back, you can spraypaint the item (provided this is possible) and that will cause the item to move to your inventory.
Food - canned food can be opened and the open can will end up in your inventory
So the item itself is fine, it just won't be picked up or taken in your hands in its current state.