Use pax. The default pax format, called ustar, preserves file modification and access times (among other things like user ID, group ID, file mode bits and extended attributes like Spotlight comments and ACLs). See pax man page here for more details.
First, create a pax archive on every Mac and copy it to the external hard drive like this:
- Open Applications>Utilities>Terminal.
Type in Terminal:
$ cd
and drag the folder where the files to be combined reside on that Mac to Terminal:

Alternatively you can type the full folder name:
$ cd /path/to/your\ folder
This will change the current folder to 'your folder'.
Archive the folder with pax:
$ cd ..
$ pax -w "your folder" > yourfolder.ustar
Use the Finder to copy the newly create archive yourfolder.ustar to the external hard drive.
Then extract the archives with pax:
Open Terminal on the Mac that has the external USB hard drive plugged in.
Change the current folder to the single folder hierarchy on the external hard drive with command cd as explained above:
$ cd /Volumes/externalHDD/path/to/single \folder
$ ls
yourfolder.ustar
yourfolder2.ustar
yourfolder3.ustar
Extract the archives:
$ pax -r -p e < yourfolder.ustar
$ pax -r -p e < yourfolder2.ustar
$ pax -r -p e < yourfolder3.ustar
$ ls
your folder
your folder 2
your folder 3
Move the files around with the Finder if you need to (the Finder preserves file modification and access times within the same volume).
(I've tested this procedure on OS X 10.8 (Mountain Lion).)