How do I remotely edit files via ssh?

You can do that via scp like this:

vim scp://user@myserver[:port]//path/to/file.txt

Notice the two slashes // between server and path, which is needed to correctly resolve the absolute path. [:port]is optional.

This is handled by vim's netrw.vim standard plugin. Several other protocols are supported.

You could do this by mounting the remote folder as a file-system using sshfs. To do this, first some pre-requisites:

sudo apt-get install sshfs      #for Debian based OS, use yum or zypper depending on your OS
sudo adduser <username> fuse

Now, do the mounting process:

mkdir ~/remoteserv    
sshfs -o idmap=user <username>@<ipaddress>:/remotepath ~/remoteserv

After this, just go into the mounted folder and use your own local customized vim.

Depending on what you mean when you say you do not have the rights to edit the Vim settings, there may be a way of using Vim on the server in the way you want anyway. If you can't change your user .vimrc (because you're logging in as a shared user, for example) but you can still create files, create it as a file called, say, Loom.vimrc and then call Vim using the -u switch:

vim -u ~/Loom.vimrc file_to_edit

You can even then use an alias: alias vim='vim -u ~/Loom.vimrc' will allow you to use Vim in the usual way, and it'll still load your custom .vimrc file. This alias won't persist after you log out, so you don't need to worry about anyone else accidentally using your customised Vim.

Depending on how many files and what kind of files you are expecting to edit, this is maybe not exactly what you want to do here, but I think it's worth mentioning. If you have to edit files in a remote server, but want to use everything you have in your own working station, then you may want to start thinking of using some kind of Revision Control system in your machines. That way, you can modify your local copies in your own machine using your software of choice, commit the changes, and then just update the local copies in the destination machine. Besides editing the files with whatever software you feel comfortable with, you have the added value of having a history of changes related to each file, which is always good.

Here's a list of Revision Control Software, just in case.