ok ok I know the methane idea is not new for a post apocalyptic setup as Mad Max Beyond Thunderdome was already tapping the methane idea... Except:
In Mad Max, the methane crudely refined from pig faeces, is only used to power the electric generator of the city (Bartertown). I propose to get a lot more out of this easy to collect/produce gas.
You want to use this gas to power your vehicle? no problem, as long as you manage to save a little bit of the current knowledge with you. This could be any of the proposed solution, or possibly something in between.
Example of usage of methane as a power source for vehicle:
The Bio-Bug has been converted by a team of British engineers to be
powered by biogas, which is produced from human waste at sewage works
across the country. They believe the car is a viable alternative to
electric vehicles. Excrement flushed down the lavatories of just 70
homes is enough to power the car for 10,000 miles - the equivalent of
one average motoring year. This conversion technology has been used in
the past but the Bio-Bug is Britain's first car to run on methane gas
without its performance being reduced. It can power a conventional two
litre VW Beetle convertible to 114mph.
2) Hybrid (vehicle or refinery)
Four-stroke engine cycle produces hydrogen from methane and captures CO2
This is an internal combustion engine repurposed to run on methane and produce hydrogen. You can decide to integrate it into an hydrogen powered motor or make a large factory/refinery which will use methane to produce hydrogen fuel for your fleet.
added bonus, you'll save the planet by capturing CO2 ... ho wait "save the planet. after the apocalypse?" ... nevermind!
And if you're after a really fast methane guzzling vehicle, check out the
Raptor is a staged combustion, methane-fueled rocket engine
manufactured by SpaceX. The engine is powered by cryogenic liquid
methane and liquid oxygen (LOX), rather than the RP-1 kerosene and LOX
used in SpaceX's prior Merlin and Kestrel rocket engine families. The
earliest concepts for Raptor considered liquid hydrogen (LH 2) as fuel
rather than methane. The Raptor engine has about two times the thrust
of the Merlin 1D engine that powers the current Falcon 9 launch
OK the last example probably require a significant amount of knowledge and infrastructure to be able to use it efficiently, but I am sure some cruder versions could be attainable by some passionate post apocalyptic engineer minded persons. The DYI version of this would probably be extremely unstable and dangerous but the Mad Max worlds inhabitants have a different attitude to risk and don't have a strong focus on health and safety so you should be ok for a while ...