The youths were charged last month with preparation of terrorist acts as they were allegedly poised to travel to Syria.
Alsyed, from Hounslow, and one of the 17-year-olds are also charged with collecting information contrary to section 58 of the Terrorism Act 2000 while the other 17-year-old is accused of dissemination of a terrorist publication.
According to the charge details, two of the youths went to the gym and paintballing as training for their plans while the other two allegedly bought flights and visas to Turkey and survival equipment.
They are all also accused of having extremist material and swapping messages online discussing how to get out to the war-torn country.
One of them allegedly had a video on his phone of battles, crusades and prisoners of Islamic State being executed.
Another is charged with having details about how to build a pressure cooker bomb.
Mr Justice Holroyde ordered the trial to be heard at Woolwich Crown Court from July 3 before Judge Christopher Kinch QC with a plea hearing on a date to be fixed in June.
He denied bail to Alsyed, who appeared before court by video link from prison.
However, the two 17-year-olds, of Middlesex and Merton, were granted bail with strict conditions, including not to use mobile phones or social media.
No application for bail was made on behalf of the 16-year-old defendant, of south west London, who was remanded in custody.