The Woodland kingdom was not strong enough to be counted as "One of the big ones", but
Lorien was! Especially because of
Galadriel,
Celeborn and their kinsmen. Not to mention Nenya.
I don't know about their "kinsmen", since as far as I know none of their kinsmen resided there in the T.A. If by "kinsmen" you mean
Sindar/
Noldor who followed them then yes, as lot of their "kinsmen" did live there.
Thranduil's
realm was certainly as large, or larger then the other three
kingdoms. They had a total population that was less then the population of
Minas Tirith and her fiefs, so we could amalgamated their population at being a few thousand, though any guesstimates would fluctuate.
Oropher's kingdom (
Mirkwood) was larger then Amdir's (
Lothlórien) by far at the time of the last alliance. The Sylvan losses in the Last Alliance were large. The Sylvanic
realms then prospered in the T.A and again built up a semblance of the splendour of their former (relative) glory. But the mass exodus after the emergence of the
Balrog in
Moria and the increasingly bellicose developments meant a lot of
Elves left for Belfalas. This haven was set up by a group of Sindar who left
Beleriand during the War against
Morgoth. I don't know if any Elves of Mirkwood left for the havens, they may have,
Legolas refers to the havens as "our" havens (i.e. Sylvanic) but he talks about the "us" Sylvan Elves as an ubiquitous group on one or two occasions, despite their separation. The Elves of Mirkwood would not have been as seriously effected by the fall of Moria as the Lorien Elves, but some may have left because of the appearance of
Dol Guldur and other hostile forces some years beforehand and possibly because of the appearance of
dwarves close to their kingdom, though the majority of the Moria exiles went to the
Grey Mountains, whilst only a fraction went to the
lonely mountain under Thráin I, though of course a larger population returned their under
Thror after the deaths of Dáin I and Fror. Some may have left simply as a matter of choice and some because of the encroachments of
Men in their affairs. They had their own exodus when Legolas set up his own quasi-autonomous realm in
Ithilien. But
Tolkien refers to the elven-haven in Belfalas as consisting of Sylvan Elves from
Lórien.
Thranduil's army, was presumably "too large" for the Orks who attacked
Isildur. These Orks were said to out-number the Dúnedain by something like 10-1, and Isildur set out with 200 men, so Thranduil's army must have been quite populous, and you must also bear in mind that he had lost 2/3 of his men in the war, and given the population replenishment in the T.A, their population would have been quite large.
One wonders then at who
Elrond means by "us". There was a represenative of Thranduil at the council, but he was there by circumstance.