You can select multiple files at one time for uploading via the Strava website. To be exact, you can select 25 files at a time - or up to 25 megabytes, and the data will upload to Strava in one click.
To do so, simply follow these steps:
1. Save the files you wish to upload to a local folder on your computer
2. Log in to Strava.com and click the orange "plus" icon at the top-right of the screen. Choose "Upload Activity".
4. After clicking "Choose files", browse to the local folder where your files are saved, and select the files you wish to upload (up to 25 files at a time).