There are lots of places on the net that offer that service, do a search on "domain forwarding" [google.com] and you'll see services that let you set up the domain you still own to forward to the hosted one.
One caveat, since you want to redirect to a specific path (/olddomain) which will in essence become the content of the olddomain.com you'll find that most of the redirection services consider that a premium service and may charge a fee that is higher than just hosting the domain with an ISP in the traditional way.
Most ISP and other free hosts won't allow nameserver information for their sites. Also, some redirection services will bring up the site under the domain name using a frames setup which results in the same site showing up under two URLs - duplicate content. I just saw this with a site that's a Yahoo store.
Check several redirect services out. I don't remember which one it was but there is one that doesn't have that problem. But I think you *might* have to use them as the registrar. It's been a while so I can't remember exactly, but one site I'm familiar with used a redirection service where only the domain name showed up at search engines. She had great rankings over with no duplicate problem at all; only the domain name showed up. They had several options available, one of which they called "cloaked redirection."
Clarification: is the domain you want to point it to regular hosting?