The following example runs a command via ssh and then get command stdout, stderr and return code:
import paramiko
client = paramiko.SSHClient()
client.set_missing_host_key_policy(paramiko.AutoAddPolicy())
client.connect(hostname='hostname', username='username', password='password')
channel = client.get_transport().open_session()
command = "import sys; sys.stdout.write('stdout message'); sys.stderr.write(\'stderr message\'); sys.exit(22)"
channel.exec_command('/usr/bin/python -c "%s"' % command)
channel.shutdown_write()
stdout = channel.makefile().read()
stderr = channel.makefile_stderr().read()
exit_code = channel.recv_exit_status()
channel.close()
client.close()
print 'stdout:', stdout
print 'stderr:', stderr
print 'exit_code:', exit_code
hope it helps