I normally type on a Dvorak keyboard, but often login to an SSH server from computers that won't let me change the keyboard layout. Is there any way to set a keyboard layout on the server-side to translate QWERTY input into Dvorak?
No. Input from keystrokes are handled by your SSH terminal application on the client machine, not by anything on the server.
loadkeys configuration as suggested by @JustinPearce will change the keyboard layout on the console of the server when you log in there physically (console-tty, non-SSH).
You could try something like:
dvorak.map.gz to the file name for the dvorak keymap. You can even set this up as a bash script to run when your user logs in via the terminal.