how to modify a transport device with an internal combustion engine with different atmospheres
Each of the cases will strongly depend on the non-atmospheric natural
resources available on each planet.

For example in an atmosphere of $\ce{O2}$ + inert gases, it would be desirable to have deposits of hydrocarbons or $\ce{H2}$ gas to be mined and pumped into your fuel tank to burn with the atmospheric $\ce{O2}$.  In each case proposed below it is assumed that the non-atmospheric reagents would be available as deposits on the planet or that they could be synthesized in a way that they are acting as batteries, storing the energy that went into their synthesis.  That said, here are some possible simplistic solutions for the different scenarios.

Scenario 1: $\ce{CH4}$ + $\ce{N2}$ atmosphere:

Here you could simply reverse the typical internal combustion engine process used in Earth-vehicles. Rather than filling your tank with hydrocarbons to be mixed and burned with atmospheric $\ce{O2}$, you would fill your tank with (probably liquid to keep the volume small) $\ce{O2}$ to be mixed and burned with atmospheric $\ce{CH4}$.  Just as with conventional internal combustion engines on Earth, the reaction products would be $\ce{H2O}$, $\ce{CO2}$, and heat.

Scenario 2: $\ce{CO2}$ atmosphere:

As $\ce{CO2}$ is already thoroughly oxidized, you would need to fill your tank with a good reducing agent.  If there were deposits of $\ce{H2}$ gas trapped within the planet, then you would mine the $\ce{H2}$ and fill your tank with pressurized $\ce{H2}$ gas (the resources required to form and store liquid $\ce{H2}$ just wouldn't be worth the trouble, though there are other ways to concentrate $\ce{H2}$ then liberate it when needed).  The $\ce{H2}$ would then be mixed and burned with $\ce{CO2}$, ideally giving off $\ce{CH4}$, $\ce{H2O}$ and heat as products.  

Scenario 3: $\ce{Ar}$ + $\ce{Cl2}$ atmosphere:

First to address is the composition of the vehicle, or at least the parts that would come into contact with the $\ce{Cl2}$ and other reactants and products, I propose a $\ce{SiO2}$ based coating for all components that would be in such contact.  For a gas-phase ignition scenario, I propose a diesel type of concept (ignition heat from compression of the mixed gases) to avoid the need for electrical ignition, metal wires, etc.  

One possibility is to use the $\ce{Cl2}$ analogously to how $\ce{O2}$ is used in internal combustion engines, namely as the oxidant.  A hydrocarbon, $\ce{CH4}$ to keep it simple, would act as the reductant.  This reaction would ideally produce $\ce{CCl4}$, $\ce{HCl}$ and heat.  The atmosphere is already toxic and corrosive so the $\ce{HCl}$ exhaust is probably OK.  

In the same manner as the $\ce{CO2}$ atmosphere, $\ce{H2}$ is another possibility.  In this case, the ideal reaction product is just $\ce{HCl}$.  

One final possibility is worth considering here.  In all other scenarios I've only proposed fluids as fuel for the combustion.  But $\ce{Cl2}$ reacts very exothermically with $\ce{Fe}$ metal.  And the ideal product, $\ce{FeCl3}$, is also a solid.  So introducing a fine iron dust in some carrier gas could actually have the advantage of ease of collecting the exhaust do be disposed of at a dedicated treatment center.  That way we wouldn't pollute the air for the $\ce{Cl2}$-breathing natives.  

Note that most of the proposed fuels here are composed of some of the most abundant elements in the universe.