Haha. When i was writing my first reply i considered if you had mixed up the Nerva and Vasimr. The thing about the irradiation is that if you can shield against neutrons, it really shouldn't be a problem. It's the neutrons that makes stuff radioactive, in a nuclear reactor. The shielding against neutrons is a lot lighter than shielding against radiation (Alpha, beta, gamma). Therefore that really wont be a problem. The biggest problem i could see about radiation would be radiation from the reactor while you are on the ground. But if you have some shielding around the reactor when you land (Hydrogen producing methane for the return trip), you should be able to reduce this to an acceptable level. If you consider that the crew will spend most of their time either in the highly shielded crew area of the vehicle or away from the landing site you should be able to make it work.

If you could make the vehicle land in a reasonable way (Aerobrakes deployed late in reentry), you could do supersonic retropropulsion. This would give you about 70 tons on the martian surface (Assuming 130 tons LEO and 825 ISP transfer from Earth to Mars), and if you do a LOX assisted liftoff at Mars you will probably only need around 10 tons of hydrogen. This would allow a total of 60 tons of vehicle dry mass. You would probably need 10 tons for an earth reentry vehicle (Modified and downscaled orion, orion has capacity for 6 we only need 4), and probably 10 tons for the NERVA you have 40 tons left. This will be split into 20 tons of crew habitat and airlocks, 10 tons of ISRU and structure, 5 tons of surface equipment (Small rover and stuff) and 5 tons of supplies (If you have recycling of water and air this might be possible). It is very barebones, but so was apollo. Science equipment could also be sent ahead of the crew on an atlas or falcon rocket.