I think you can get rid of the nohup. Just the & at the end of the line should start the processes in the background. If you want to wait for all processes to finish just put a line below that says "wait" without the quotes.
ssh remoteserver1 script-name &
ssh remoteserver2 script-name &
ssh remoteserver3 script-name &
EDIT: Just thinking that your error message might be related to something different. Are your scripts trying to read from stdin or write to stdout?
SIGTTIN and SIGTTOU
The SIGTTIN and SIGTTOU signals are sent to a process when it attempts to read in or write out respectively from the tty while in the background. Typically, this signal can be received only by processes under job control; daemons do not have controlling terminals and should never receive this signal.