Are translators of mathematical texts (books or articles or whatever) from a foreign language into English in demand today? Specifically, I'm interested in German and Russian. If they are, then what kind of organizations (or what specific organizations) are interested in such translators? Do people working for those organizations usually combine the translation job with a teaching and/or research job?
It is hard to tell if they are really in demand today. I have no statistics at hand but I guess that the demand is (slightly) declining since most books are written in English these days. But there are of course counterexamples to this statement. There has been a popular German book on functional analysis, being first released in 1985. In 2016 it has been translated into English, see below. I studied at a German university and the recommended books in my undergraduates were mostly German books, only a few being translated into English. It is hard to tell whether it is worth it to translate them because there are already a bunch of English books on "basic" subjects.
What kind of organization is interested: Probably the authors are interested, but not for monetary reasons, but so that more researchers in the whole world can read their books. The publisher should also be interested, selling more copies. And of course the researchers. I'd wish there would be an English copy of "Quelques méthodes de résolution des problèmes aux limites non linéaires" by J.-L. Lions. In general, the translators are not working directly for the publisher. They are active mathematicians in research and/or teaching at a university. Most of them are no regular translators (see my examples below), having translated only one book so far. But you can look up Richard A. Silverman, who translated a dozen Russian books for Dover.
From German into English:
-"Linear Functional Analysis" (2016) by H.W. Alt: "The present book is the English translation of a previous German edition, also published by Springer Verlag. The translation was carried out by Robert Nürnberg, who also did a marvelous job at detecting errors and mistakes in the original version." Robert Nürnberg is a mathematician at the Imperial College London.
-"Vector Analysis" (2001) by K. Jänich: "Speaking of translation, I would like to acknowledge the excellent work of Leslie Kay in translating the German text into English. We have exchanged detailed e-mail messages throughout the translation process, discussing mathematics and subtleties of language." Leslie Kay is a mathematician at Virginia Tech.
From Russian into English:
-"Lectures on Partial Differential Equations" by V.I. Arnold: Translated by Roger Cooke, University of Vermont.
-"Mathematical Aspects of Classical and Celestial Mechanics" by V.I. Arnold et al.: Translated by A. Iacob, Brandeis University
-"Mathematical Methods of Classical Mechanics" by V.I. Arnold: Translated by K. Vogtmann, Cornell University, and A. Weinstein, University of California at Berkeley
Marvin's answered about demand of translations fueled by potential readers in English speaking countries, but there is another (maybe larger) source of demand: authors from non English speaking countries.
Most researchers all over the world are required to publish articles in international journals, nearly always written in English, and not all of them have the ability to write in English. I've seen offers of professional services marketed to these researchers.
However, keep in mind that that marked could be dwindling in the next decades, since the level of English of young grad students is way better than those of older faculty on their forties or fifties.