Nothing is written about Elladan and Elrohir after the War of the Ring except that they remained in Rivendell, and Celeborn joined them there. Perhaps they chose mortality, or they had not yet decided. Perhaps they sailed to the West with Celeborn.
I imagine they aided Aragorn until he had subdued all of Gondor's enemies and saw Arwen as much as they could before finally sailing to Aman. Maybe it's just because I think it would really suck for Elrond to lose all his children.
What do you think they did? There are no right or wrong answers here.