Why is Russia translated to 俄罗斯(E Luo Si)? The Chinese Wikipedia article describes the name of Russia, and many of its historical Chinese exonyms. 


  按照俄语发音“Россия”，其名称应翻译为“羅西亚”。元朝时根据蒙古语译为「斡羅思」[b]，到清朝初年许多文献中曾称为「羅剎」[c]，但在以国家相称时则多译为「鄂羅斯」[d]或「俄羅斯」。清乾隆年间官修《四库全书》时将其正式统一为“俄羅斯”或简称“俄国”，自此沿用至今。[12] 日本漢字與朝鮮漢字則將俄羅斯稱為「露西亞」（日语：ロシア roshia */?，韓語：노서아 noseoa */?[e]），此譯名較為接近俄語原始發音。


However, while the "罗斯" part corresponds to the "Rus" part of the name, the "俄" part seems to have no corresponding phoneme, either in Russian or any of the other language I have looked up.
the "俄" part seems to have no corresponding phoneme, either in Russian or any of the other language I have looked up.


Yes it's peculiar in Chinese. It's related to the Mongolian.

Reference: 郭文深.俄罗斯国家名称变迁考——从“罗刹”到“俄罗斯”

Summarize it in short:

From Yuan Dynasty, the Mongolian translated 罗斯 as oros (but not ros) followed by the Mongolian pronunciation habit, and then translated into Chinese character as 斡罗斯. In Mongolian, there's no words started from [r], such words are usually borrowed words. Then for these words, in order to make it conform to Mongolian pronunciation rules and incarnate Mongolian vowel harmony, the strong vowel of the first syllable will be brought forward. Then 罗斯"ros" became oros, then 斡罗斯.

In Qing dynasty, the Manchu didn't have direct contact with the Russian, they used the translation (especially the transliteration) of the Mongolian which is the intermediary between them. For Chinese characters they used 鄂罗斯 and 俄罗斯, until the Emperor QianLong unified them into 俄罗斯.