Self-maintenance. And it might be they only need fuel to kickstart the reaction that continuously keeps them moving, because... Science!
They only thing they would need fuel for is their flamethrower. Their nuclear generators could presumably last for however long SCIENCE! demands.
Also, they can turn themselves off and on, so they likely spent most of that time in standby move, saving power.
Mr. Gutsy's would have armor plating, and most likely they would have been in stasis until awoken at some point after the great war. Mr. Handy's would also have some sort of armor plating as well, most likely less so than a gutsy... but enough to keep them going. I'm sure at some point their auto maintenance program kicks in and they return to their pods. That and wastelanders probably get their hands on them as well, keeping them as protection, possibly trading them. Some even get enough know how to reprogram them to be more aggressive and after their owner gets inevitably killed... they go off and attack things on sight.
That'd be awkward, considering Cods can just screw around after all this time.
There are also a ton of cars just lying around. They're probably siphoning fuel out of them and raiding old gas stations.
Maybe they are powered by nuclear fuel and they're just collecting the radiation in the air and turning it into fuel inside themselves, so we don't see it.
Or it's SCIENCE!
Robots can fix themselves and go indoors to avoid the harsh elements. Cars just sit there where they were