Known generation
I
Enel - Enelya
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II
T
C
E O?
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III
Olwe Elwe
Elmo
?
?
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Earwen Luthien Galadhon
Cirdan
Eol
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Angrod Galadriel Dior
Celeborn Galathil
Maeglin
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Orodreth Celebrian Elwing
Celebrian Nimloth
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Gil-galad
Elrond
Elwing
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Elrond
Persons appearing twice are in color. Note that Galadriel and Celeborn produce Celebrian, and Nimloth and Dior produce Elwing. Talk about kissing cousins! Note that there might be more than one generation between what I have labelled I and III. If Oropher (Legolas' grandfather) is also a "kinsman of Thingol", as are Cirdan and Celeborn, we have only a few choices.
1) He is clearly Sindar, and apparently isn't fond of the Noldor (see his canon reaction to Gil-galad during the formation of the Last Alliance). Olwe's line becomes "Noldorized" within a few generations (Earwen marries a Noldor prince -- Finarfin, who, himself is half Noldor, half Vanyar), so that knocks that line out.
2) He can't be a direct descendent of Thingol (Elwe), since Thingol's line has no branches (each child had only one child until we get to Elrond and Elros)
3) He COULD be a descendent of Elmo, which would make him relatively closely related to Celeborn, except it would also make him closely related to Elrond through Nimloth, and in canon there is no ties of kinship mentioned between Elrond and Oropher (and, again, Oropher refuses to march under Gil-galad's banner, even though Elrond is Gil-galad's herald)
4) Eol was a major asshole and fortunately his son had no heirs. Oropher could be a distant relation of Eol (branching off the E line somewhere previously), and that would give lots of bad blood between Elrond and Oropher since Maeglin tried to kidnap Elrond's grandmother and father in Gondolin. Glorfindel would have witnessed this, and would lead to some interesting stories he could tell Legolas about his distant relatives behaving badly.
5) Oropher could be related off the C line, which would make him a close relative of Cirdan. We know Oropher once lived near the Grey Havens, and was probably a refugee on Balas during the War of the Jewels, so this could make sense. But if Cirdan, who was very well respected, was a close relative of Oropher, how come he couldn't get Oropher to get in line during the Last Alliance?
6) Oropher could branch off even earlier, in the hypothetical line labeled O.
I have chosen #4 in this universe -- you mileage may vary.