Sharing happens when one server can either use or duplicate the content from another server. Note that I don't have to upload them. I could make a folder on my local machine shared, for instance.
Uploading happens when one or more files, usually more than just text, are transferred from a local machine to a server. Note that they don't have to be shared; I can upload files to DropBox without sharing them with anyone.
Sending happens asynchronously, for instance, with email.
Post comes from a particular HTTP verb, and usually means submitting something over the internet. You don't have to use HTTP to share or upload files; you could use FTP, for instance.
You've said that outh is managing whatever it's doing with the services. Is it sending images to those services? Posting them over HTTP (unlikely)? Uploading them to their servers? Or just sharing those files and relying on the services to come get them? Or is it perhaps streaming them?
This is why I avoid the word "manage" when programming or talking about apps.
If you're talking to non-tech-savvy people, share would be fine. They'll understand that terminology if they've come across Facebook.
You could also try http://programmers.stackexchange.com.