Some specific version of the F-16 can carry the AIM-7 on station 3 and 7. They need special pylons. Without looking, the Egyptians F-16 (specifically their block 40), Iraqi block 52+, ROCAF F-16A block 20 and USAF F-16A ADF. I am sure there are others.
AIM-7 can't be carried on station 1, 2, 8 nor 9. Only station 3 and 7 AFAIK, because of weight
The AIM-120 can be rail launch, if you look at the missile it has "hooks" that go on the rail.