Dozens of demonstrators carrying placards jeered the ICC team, led by Zimbabwe's Justice Ahmed Ebrahim, as they entered the hearing venue at Nairobi's Stanley Hotel. The hearing had been adjourned on May 19.
After the first two witnesses testified in public, journalists were barred from the room as the third witness, whose identity was concealed, gave his evidence behind closed doors.
In her evidence, Canadian national Caitlan Patterson, who had a two-year affair with Odumbe, claimed alleged Indian bookmaker Jagdish Sodha had visited Kenya in September 1999.
"He came to our house and I made him a cup of tea and he was surprised that I could make very good chai (Swahili word for tea)," Patterson told the tribunal.
Patterson said Sodha used to telephone their house, and that she accompanied Odumbe on trips to Zimbabwe, Namibia and India.
Odumbe, who has denied receiving payments from an Indian bookmaker to fix matches in 2002, faces a minimum two-year suspension or a possible life ban from the game.