Can I host multiple sites on a single Linode server a la Dreamhost?

You can point as many domains as you like to a single IP address; the VPS has nothing to do with this unless you want SSL.

Absolutely. The VPS emulates the hardware of a server. What you install on that is up to you. Handling multiple domains is a fairly common webserver function.

What you want to look into is something like Apache2's VirtualHost configuration. You can find some basic setup details (tailored for an Ubuntu 10.04 installation on Linode) here:

http://library.linode.com/lamp-guides/ubuntu-10.04-lucid

In particular the section on configuring name-based virtual hosts.