You must be in the same room as the crates. Go to Position -> Items, then select the option to equip the crate (make sure you haven't already got something equipped - if you are selecting your hands, your hands must both be empty, because the crate requires both hands to lift). Then board the ship you want to deposit the crate on, go back to Position -> Items, click on the crate, and select the option to drop it.
If you do not have the option to equip the crate, but are in the same room and have your hands free, compare the amount your strength allows you to lift with the weight of the crate; your skill may be too low to move it, in which case you would need something like a gravsled, or to remove the items from the crate and move them manually.
“There are 6 Carrying Positions: Head, Chest, Right Hand, Left Hand, Back and Belt. All characters have a max Carrying Capacity in which they can carry items without the help of Backpacks or Belts. This Limit is calculated as follows: