I am working on an internal authentication system for users of a set of of RESTful web applications. Our intention is that a user should be able to sign-on once via a web form
You do not need OAuth for SSO services.
The primary use/advantage of OAuth is, as you know already, granting access to a 3rd party app to access/use your resource in a controlled manner.
Rather than having an authentication/authorization server that you would need for OAuth, why not use a single log in service across all your APIs. An OAuth access token is totally different from what you need.
As far as I understand, what you can have is something like OAuth in a way that your server vends out tokens to the app. (I'm assuming that it's a totally internal system, so tokens cannot be misused).
So basically what I'm proposing is:
In short separate the login + token generation + token verification into a different module. All APIs should use this module for login/token verification.
What I have proposed here works like OAuth but all security aspects have been stripped down since you want to use it in a private cloud.
Oauth supports multiple different kinds of flows. You can use the client crendentials flow from Oauth 2.0 to avoid asking the user to grant permission for every app (this is intended for the cases where you control both the server and the app or where you want to preauthorize certain apps). This post does a good job explaining everything: http://tatiyants.com/using-oauth-to-protect-internal-rest-api/