كتب : Hatem Maher
The hosts found no difficulty in overcoming Banks, who held them to a 1-1 draw in the first leg.
Egyptian international forward Eid put them ahead after 18 minutes when he converted a penalty.
Striker Abdul-Ghani doubled Hodoud's lead five minutes before the break when he pounced on the rebound after his initial header was parried by Banks keeper into his path.
Eid scored his second of the night in the 53rd minute after heading home a cross from Abdul-Ghani.
Mohamed Hamed added the fourth on the hour mark with a powerful shot from inside the area and Abdul-Ghani completed the rout with a close-range effort in stoppage time.
Hodoud, who are steadily climbing up the Egyptian Premier League title after recovering from a poor start, will face Tanzania's Simba in the next round.
"We had problems in the first half of the season but we have regained our top form," Abdul-Ghani said in a television interview after the match.
"Everybody was concerned but I can assure them now that this is the real Hodoud."