I use copymysports to sync with Strava. http://www.copymysports.com/ Appears automatically on Strava usually within an hour or so of syncing my device with GC. Dunno about Training Peaks.
Training peaks is able to connect to Garmin Connect directly. Personally I have no experience with this, because I don't use Training Peaks.
You can get some additional information via DCRainmaker: training-automatic-connect.html