Looking at the tags it seems you are considering Azure AD. Good choice. Azure AD allows developers to secure their SAAS APIs and Web/Mobile Apps. Azure AD satisfies all the requirements that you've described - it even has client SDKs for the popular platforms. The following should see you through:
- Authentication scenarios supported by AAD (http://msdn.microsoft.com/en-us/library/azure/dn499820.aspx): will answer questions like - how can my mobile app access my multi-tenant web api on behalf of the user, or how can my web app sign-in the user as well as receive a delegated token to access my web api
- AAD integrated multi-tenant SAAS application sample (https://github.com/AzureADSamples/WebApp-MultiTenant-OpenIdConnect-DotNet): covers special techniques for multi-tenant apps
- Authorization using group membership (https://azure.microsoft.com/en-us/documentation/articles/web-sites-authentication-authorization/): describes how you can perform authorization in your application per the group membership of users.
Enjoy. Hope this helps.