I have created a sample api by using djangorestframework which worked fine and I could use browsable api without any problem. Then I added outh2 authentication as mentioned on official website which also worked fine. I can use following to get access token.
curl -X POST -d "client_id=YOUR_CLIENT_ID&client_secret=YOUR_CLIENT_SECRET&grant_type=password&username=YOUR_USERNAME&password=YOUR_PASSWORD" http://localhost:8000/oauth2/access_token/
Web browsers don't generally let you set custom headers, so there's no way you can provide your OAuth token.
In general, if you want to use the browsable API then you need to allow session based (i.e. cookie based auth).
You can allow both authentication methods, perhaps restricting session auth for development if that's necessary.
I hope that helps.