How do I secure REST calls I am making in-app?
Securing a javascript client is nearly impossible; at the server, you have no fool-proof way to differentiate between a human using a web browser and a well-crafted script.
SSL encrypts data over the wire but decrypts at the edges, so that's no help. It prevents man-in-the-middle attacks, but does nothing to verify the legitimacy of the original client.
OAuth is good for securing requests between two servers, but for a Javascript client, it doesn't really help: anyone reading your javascript code can find your consumer key/secret, and then they can forge signed requests.
Some things you can do to mitigate API scraping:

Generate short-lived session cookies when someone visits your website. Require a valid session cookie to invoke the REST API.
Generate short-lived request tokens and include them in your website HTML; require a valid request token inside each API request.
Require users of your website to log in (Google Accounts / OpenID); check auth cookie before handling API requests.
Rate-limit API requests. If you see too many requests from one client in a short time frame, block them.
I have an application that has a "private" REST API; I use RESTful URLs when making Ajax calls from my own webpages. However, this is unsecure, and anyone could make those same calls if they knew the URL patterns. 
What's the best (or standard) way to secure these calls? Is it worth looking at something like OAuth now if I intend to release an API in the future, or am I mixing two separate strategies together? 
I am using Google App Engine for Python and Tipfy.