With OAuth, the token is generally passed in the request headers. You may wish to try something similar to the following, for both POST or GET:
POST: curl http://api.localhost/write -H 'Authorization: Bearer ACCESS_TOKEN'
GET: curl http://api.localhost/read -H 'Authorization: Bearer ACCESS_TOKEN'
The value part of the Authorization key/value pair can vary by REST service provider. With Github, for instance, the header key/value pair looks like this:
curl -H "Authorization: token your_token" https://api.github.com/repos/user/repo
You may need to consult the webservice provider docs for details.