How do radio communications work en-route for intercontinental flights over the oceans?
As Ron mentions in the comments aircraft flying transatlantic routes (or really any long route for that matter) may use HF radios operating in the 3-30MHz range to communicate over long distances. HF radio waves have the ability to "skip" off the ionosphere if directed properly and thus propagate over the horizon and beyond line of site. 

You can find some various frequency info here.

Honeywell also offers at least one satellite based solution.

You can also find a lot of good info here under the "communication" tab.

As for knowing the exact position of the an aircraft, this answers covers most navigation methods out there. 

This thread quotes FL300 (30,000 Ft.) as the minimum altitude for continuous coverage across the Atlantic as does ymb1's answer here (route dependent).