How can I run arbitrarily complex command using sudo over ssh?

A trick I use some times is to use base64 to encode the commands, and pipe it to bash on the other site:

MYCOMMAND=`base64 script.sh`
ssh user@remotehost "echo $MYCOMMAND | base64 -d | sudo bash"

This will encode the script, with any commas, backslashes, quotes and variables inside a safe string, and send it to the other server. On the other side, base64 -d will decode the script and feed it to bash to be executed.

I never got any problem with it, no matter how complex the script was. Solves the problem with escaping, because you don't need to escape anything. It does not creates a file on the remote host, and you can run vastly complicated scripts with ease.

Simply,

ssh root@host << EOF
some
lines
of
code 
but be careful with \$variables
and \$(other) \`stuff\`
EOF

One thing I often do is use vim and use the :!cat % | ssh somemachine trick.

I think the easiest solution lies in a modification of @thanasisk's comment.

Create a script, scp it to the machine, then run it.

Have the script rm itself at the start. The shell has opened the file, so it's been loaded, and can then be removed without problems.

By doing things in this order (rm first, other stuff second) it'll even be removed when it fails at some point.

You can define the script on your local machine and then cat and pipe it to the remote machine:

user@host:~/temp> echo "echo 'Test'" > fileForSsh.txt
user@host:~/temp> cat fileForSsh.txt | ssh localhost

Pseudo-terminal will not be allocated because stdin is not a terminal.
stty: standard input: Invalid argument
Test

Are you aware that you can use sudo to give you a shell where you can run commands as the chosen user?

-i, --login

Run the shell specified by the target user's password database entry as a login shell. This means that login-specific resource files such as .profile or .login will be read by the shell. If a command is specified, it is passed to the shell for execution via the shell's -c option. If no command is specified, an interactive shell is executed. sudo attempts to change to that user's home directory before running the shell. The com‐ mand is run with an environment similar to the one a user would receive at log in. The Command Environment section in the sudoers(5) manual docu‐ ments how the -i option affects the environment in which a command is run when the sudoers policy is in use.