We have a custom built web app backed by a REST API. We already have existing user accounts that are created via our system. We've just recently integrated Domo to do reporting and they recommend Okta.
Is it possible to get have users sign in on our site and in the background also sign them into Okta via an API call/OAUTH request etc?
Yes it is. The methods are available via the API, and I just created app that demos exactly this in Python. Check out http://developer.okta.com/docs/api/resources/authn.html for links to test stuff in Postman. My basic approach was to have Okta be the system of record, but it can certainly be the other way :)