You can try un-checking "Ignore Permissions", but that may not fix it per below.
For any external disk (be they USB or firewire), each time you (re)connect the disk, File-GetInfo will show a check-mark by "Ignore Permissions" (meaning any user can read-write anything on the disk). For details, see
http://discussions.apple.com/thread.jspa?threadID=1435119
If you un-check "Ignore Permission", it will not remember it the next time you connect it. So this may only work if you leave the usb-drive connected all the time, and perhaps only if the box never goes to sleep (low power mode). That is, upon waking from sleep, I'm not sure if it will ignore permissions or not. In any case, you'll wear out your disks and mac if you tell it never to sleep as it will run at full power 24/7, and some disks continue to spin at full speed even if you put a check by "allow disks to sleep" (though most newer usb mechanical disks seem to power down).
In any case, what I would try is:
(1.) Turn on journaling for the usb-disk if it's mechanical. (If solid-state or flash, then leave journalling off in Disk Utility).
(2.) Save your data, then erase the entire disk and give it a very simple name with no spaces like "USB-DISK". After it re-appears, un-check "Ignore permissions".
(3.) Try writing to the disk without using AFP and verify that works.
(4.) Now try writing with AFP (I assume from another mac) assuming you turned on "File Sharing" on the mac with the usb-drive.
(5.) If still no go, you might try enabling "Windows file sharing" on the mac with the usb-drive, and on the remote boxes use smb://blah instead of afp://blah.
You might have to create a symlink in your home dir to navigate to the usb-drive:
Utilities -> Terminal and type the following:
ln -s /Volumes/USB-DISK USB-DISK
mkdir /Volumes/USB-DISK/tmp
chmod 777 /Volumes/USB-DISK/tmp
If you can't write to top level, try writing to the tmp folder created above.
If still no go, I would erase and reformat the USB-DISK to dos-format (Fat32) and try samba again, as that should get rid of all permissions issues. Note however you cannot write a file larger than 2gig in size on a fat32-format disk.
There is a ntfs-3g extension to let you write to NTFS-formatted disks that might help if you need to write files bigger than 2gig to the usb-drive.
All the above is just educated guessing... I have not tried any of it.
Give us some specific detailed examples of what kind and size of files you want to write, how often, and the general scheme of what you are trying to do for more help.
