If you have a shell account (as mentioned above) I would simply tar up the files you want to transfer:
(In home directory on old host)
tar -cf newtarfile.tar *
This will tar up all files in current directory to a file called newtarfile.tar
Then I would Gzip it... outta habit mostly.
Then I would SFTP the file over to dreamhost.
(or whatever your user and server are)
Then you cna exectute a 'put newtarfile.tar.gz' command and send the files over to dreamhost.
Lastly. Untar/unzip via a 'tar zxvf newtarfile.tar.gz' This will extract all contents to the current directory. If you want the files in another directory make sure to move (mv) the file first.