What are my options for using the same JavaScript code to validate both on client side and on server side (Node.js)?
None, you are validating entirely different criteria on the server-side. Client-side validation is purely user-acceptance criteria and has nothing to do with security. Server-side validation almost exclusively concerned with security.
Take a look at revalidator. It is described as "A cross-browser / node.js validator used by resourceful and flatiron."