Is the Russian word "ёлка" related to the English word "yule"? "Yule" is related to Old Norse "jol," which refers to an old pagan feast of midwinter. There could easily be some Norse words surviving in Russian, so it is not too far-fetched. And it isn't hard to imagine the English word "Yule log" referring to a fir wood, as the Russian word does.
Original word is "ель" and in all Balto-Slavic languages there exists a word sharing the same original root and used as a term for the conifers. Here's a quote:
церк.-слав. ѥла (греч. ἐλάτη), русск. ель, укр. єль, їль, яль, болг. ела́, сербохорв. jе́лa, словенск. jêl (род. п. jelȋ), др.-чешск. jedla, чешск. jedle ж. «пихта», словацк. jedľa, польск. jodła, в.-луж. jědla, н.-луж. jedła. Первонач., вероятно, древняя индоевр. основа на -о ж. р. Родственно др.-прусск. addle, лит. ẽglė, латышск. egle «ель»
As for "jol", here's another quote:
From Old Norse jól, cognate with Danish, Norwegian, Swedish jul, Icelandic jól, Old English geōl and English Yule, from Proto-Germanic *jehwlą, perhaps from Proto-Indo-European *yekə- (“joke, play”).
As you can see, the answer to your question is "no, these words are not related". Also I want to noticed that both quotes can be found very easily and it is always better to try to google such things before asking questions here.
Just like on any Stack, the attempt to take some actions before producing a question is welcome.