hmm..chlorine is above the other two(Br and I) in the group 17 elements, thus its more reactive and it is very much capable of kicking off the other two.
in the solution, bromine and iodine are diatomic,and since its diatomic (two moles of the same element in a bond = equal electronegativity = 0 dipole moment) its non-polar. logically, it will dissolve better in a non-polar solution than in a polar one (like dissolves like), which means when you mixed a non-polar solvent to your solution (of NaCl,Br2,and Cl2), you're actually exrtacting the Br2 and Cl2) from it.
i think all the non-polar solvents you gave are suitable solvents.