In addition to his three sons, Eldoran is also the grandfather of Amelia Wil Tesla Saillune, Gracia Ul Naga Saillune, and Alfred Saillune. He presumably had a wife as well, but she is never mentioned.
Although he is technically still the king, Eldoran is old, sickly and bedridden, so Philionel (his oldest son) has taken over the day-to-day duties of the king.
During the events of novel four, it was said that Eldoran was living in complete denial about the whole thing, refusing to believe that Christopher would try to usurp Phil's claim to the throne, and that his refusal to believe that was the only thing keeping him alive.
Not much else is known about Eldoran, as he never actually appears in the anime or the manga, and is talked about only briefly in novel four.