Editing RTF files in text mode

I presume you want to hand-in a nicely formatted document, and the use of RTF your proposed solution. There are actually much better ways to format documents on a Unix system. The traditional way, which is likely to be available on your system out of the box, is to use troff (nowadays ditroff or its GNU equivalent groff). This allows you to markup the text using commands like \fBbold\fP and \fIitalics\fP. This is the system used for formatting manual pages. To convert the markup into PDF, install Ghostscript, and use a sequence like the following.

groff -Tps mydocument.ms >mydocument.ps
ps2pdf mydocument.ps mydocument.pdf

However, if you want to learn a system that you can build-on, I suggest to learn LaTeX. This has a more intuitive markup language (e.g. you write \section{My Section Title}) as well as thousands of add-on packages and fonts. Most Mathematics and Physics papers are written in it. In this case, the command you would use to convert your document into PDF would be something like.

pdflatex mydocument.tex

pandoc can convert a variety of markup texts into a wide variety of formats, including RTF.

Pandoc is a Haskell library for converting from one markup format to
another, and a command-line tool that uses this library. It can read
markdown and (subsets of) Textile, reStructuredText, HTML, LaTeX, MediaWiki
markup, and DocBook XML; and it can write plain text, markdown,
reStructuredText, XHTML, HTML 5, LaTeX (including beamer slide shows),
ConTeXt, RTF, DocBook XML, OpenDocument XML, ODT, Word docx, GNU Texinfo,
MediaWiki markup, EPUB (v2 or v3), FictionBook2, Textile, groff man pages,
Emacs Org-Mode, AsciiDoc, and Slidy, Slideous, DZSlides, or S5 HTML slide
shows. It can also produce PDF output on systems where LaTeX is installed.

I don't believe there is, your question is similar to this:

Using Vim to edit Microsoft Word files | Stack Overflow

If you could use LaTeX, then converting them to rtf shouldn't be too difficult.

It would help to explain why you're trying to edit rtf files; the solution is probably going to look something like:

1. scp (or ftp or samba or what not) transfer the file to your local machine

2. Edit file locally

3. Upload finished file

Alternatively, installing X11 (and possibly vnc) on one of those machines would seem the way to go. Another option would be to convert them to html with Open Office (which I believe can do batch jobs from command line), edit them, and then convert them back. But the end result is the same; I've never seen or heard of a cli editor that can reasonably edit *.rtf files directly (short of editing the very large files themselves.)