I am translating an academic paper to English. However, most of the sources cited at the end, are in other languages (e.g. Russian). Do I need to translate the list of references into English as well?
You need to keep the reference in the original language, so that people can find it if they want to look for it. However, it's also useful for the readers to have the titles translated into English, so they can understand what they mean. Many journals specify exactly how you should cite foreign-language references this in their style guides, and many do say that you should include both translated and original titles.
To take an extreme example, Google translates the book title
Winning Ways for your Mathematical Plays
into German as
Gewinnmöglichkeiten für Ihre mathematischen Spiele
(which, with my limited knowledge of German, I think is a reasonably good translation). Looking these words up in the dictionary might then produce the literal translation back into English of
Profit Opportunities for your Math Games,
from which it would be moderately hard to identify the correct source.
Another answer suggests (especially if it your own article you're translating) replacing foreign-language sources with equivalent English ones. I think this is intellectually dishonest, as a source that's cited in the original should also be cited in the translation. However, I don't see anything wrong with adding equivalent English sources, along with a note that they were added in translation. (There isn't any requirement that you do this, of course, but it would be of help to the reader.)
The general principle here is to think about your reader. Imagine a person reading the translated article who needs to refer to one of the sources. Would it be beneficial for them if the source is translated to the language they can read?
Yes, it probably would be beneficial, so yes, consider translating / transliterating the references. Also, provide a doi / direct link to the source if possible. If you are also an author of the original paper, consider taking another look on the sources to identify those which are more likely to be accessible for your new wider audience. Consider removing references available exclusively in Russian and replacing them with equivalent references available in English translations. Your main aim at this stage should be to make your paper readable, not to self-promote your past papers.
Also, contact the editor / secretary of your target journal for clarification.