The team reported live on the developing situation as rocket propelled grenades and small arms fire went off nearby.
"It is truly an honour to be appreciated and recognised by such a prestigious awards institution," Odeh said.
"It is a testament reflecting the hard work and efforts by not only me, but by Ashraf, who continued and pressed forward under such difficult conditions, and Iyad, who ultimately kept the camera rolling."
Amritti said the team members were pleased that their reporting had been able to show the harsh conditions that Gazans continue to face.
"We aim, and continue to aim to highlight how tough life is in Gaza. Yes, it is tough for journalists, but our reports have highlighted that residents living here are under a lot of pressure," he said.
"All Palestinians continue to be [under pressure] despite the factional divisions that was witnessed last year."
Al Jazeera received nominations in every news category at the prestigious ceremony, including the "Best News Documentary" award for Inside Myanmar – The Crackdown.
The programme was made by Tony Birtley during the military government's repression of pro-democracy protests.
James Bays also took second prize in the "Best TV Item" category for his reports following Taliban fighters in southern Afghanistan.
Tony Burman, Al Jazeera's managing director, said: "For me, the award demonstrates the commitment of AJE's [Al Jazeera English] staff to giving a voice to the voiceless, of telling vital stories that are not on the agenda of the western news networks."
Al Jazeera English was launched in November 2006 with broadcast centres in Doha, Kuala Lumpur, London and Washington DC.