I found this in The Peoples of Middle-earth, The Appendix of Languages, pg 79
Quote:
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For there were other Elves of various kind in the world; and many were Eastern Elves that had hearkened to no summons to the Sea, but being content with Middle-earth remained there, and remained long after, fading into fastnesses of the woods and hills, as Men usurped the lands. Of that kind were the Elves of Greenwood the Great; yet among them also were many lords of Sindarin race. Such were Thranduil and Legolas his son. In his realm and in Lorien both the Sindarin and the woodland tongues were heard; but of the latter nothing appears in this book, and of many Elvish name s ofpersons or of places are used most are of Grey-elven form.
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According to this, most of the Elves in Mirkwood (Greenwood the Great) were Avari (Eastern Elves).