REST API call in JavaScript/AJAX that authenticated Oauth2.0 - repost

I've got 3rd party system that supports REST API call via Oauth 2.0. I need a page set-up (I can host this myself, just been the Code) that when visited takes a parameters from the URL (e.g. it gets the ID parameter from the following URL [login to view URL]). And does and REST call into the 3rd party updating an objects record (I need to update one field against the object using a POST). I need to do this using client side scripts such as JavaScript, AJAX etc I’ve trying building this myself but a limitation that I’m facing it that because it’s a cross domain update, so it looks like I need to use JSONP which I’m not experienced with.