From the passage, you can guess that the word odious means

the committing of terrorist acts in the perpetrator's own country against their fellow citizens.

the conditions that made the byzantine empire vulnerable to attacks by the muslin turks were the sack of constantinople by western crusaders, the conquests of the sultanate of rum, presence of rival kingdoms and finally the set up of fiefdoms at the empire which were owned by the ghazis (turkish warriors).