PHP Curl and nuSOAP can run on shared hosting?
Of course, the real question, however, is "do(es)
your hosting provider(s) support it?
with curl can transfer data to another server?
Absolutely. You would treat the "receiving" server as the client and the sending server as the host.
even from VPS to Shared server or vice versa?
Yes sir. A server is a server is a server (kind of, lol), but YES. Again, however, does the hosting provider support it.
This is a whole other can of worms. In all honesty, I could explain many different ways, however, your best bet would be to search google for phrases like:
"server to server transfer using curl" or
"curl server to server" or
"how do I transfer files using curl"
or any variation thereof