Hi,
It is my understanding that the RESTful API is not supported by Eloqua itself.
When trying to get the activity's you indeed have those types you stated.
You could also get the external activities but i'm not sure if that's what your looking for?
The call for the default ones is:
https://eloqua.com/API/REST/2.0/data/activities/contact/{ID}/{TYPE}?startAt={START_TIME}&endAt={END_TIME}&count=200
I did ran into some time issues when testing this for a project.
You could try to take times in the future to exclude that problem.
Hope i've been any help to you.