He was the first Connacht player to make 100 appearances for the side, while his points tally remained a record until being surpassed by Jack Carty in 2023.

Elwood also made a single appearance for international invitational side the Barbarians before being capped by Ireland.

Elwood made his debut for Connacht against Scottish North & Midland, at inside centre, on 18 September 1989.

By the time he made his final appearance, against Sale on the 24th of April 2005, Elwood had scored 8 tries, 141 conversions, 7 drop goals and 268 penalties, a total of 1,152 points.

He made his last appearance for Ireland coming on as a substitute in their play-off loss to Argentina at the 1999 World Cup in Lens.

Eric also participated in the inaugural 1993 Rugby World Cup Sevens held in Murrayfield, where the Ireland Squad reached the semi-final, losing out to eventail runners up Australia.

Connacht lost their first five matches in the pool stages, claiming losing bonuses in both of their ties with Gloucester.

In the final game of their pool, however, they managed an upset, beating Harlequins 9–8 in the Galway Sportsgrounds, which prevented the Premiership club from topping the group, and knocked them down into the Amlin Cup.