Multi-Fuel vehicles fall into two broad categories, coequally termed Pistons and Fans. Piston units, more properly, adaptive internal combustion (A.I.C.) enginess - are computer controlled, detect what fuel is in use, and and adjust the timings accordingly, but otherwise operate akin to a standard gasoline engine. Conversely, "fans" are based on turbine technology - powered by heat, steam, and whatever will burn.
Piston A.I.C. engines show distinctly better fuel economy. Their parts are also a bit less exotic - turbine blades are chunks of metal grown like crystals for superior strength, while a cam shaft can be turned out on any properly set metal lathe. However, they do tend to have somewhat more parts - spark plugs, fuel lines, timing systems, injectors and so forth. They tend to work best when using only one fuel type at a time, and often require extra maintenance to remove deposits or flush lines to avoid corrosion or the timing set off. Perhaps the most problematic element is since the fuel flow, combustion, and exhaust rates are computer controlled, these types were far more likely to have been compromised by the EMP.
Turbines simply need heat, and will work with mixed fuels of any grade, or even mixed types at once. Some even get hot enough to use paraffin (which is solid at 134 degrees F / 57C) or use natural oils unadulterated. Rather than being direct drives like A.I.C.s (usually) are, turbines act as electrical plants for electric other motors - so there is less to worry about in ways of a transmission or a single drive shaft. This also means that they're the right choice for vehicles than need a lot of electricity for systems like radar, rail guns, anti-missile lasers or large communication arrays. The trade off is, they're hotter, (essentially a small jet engine running a power plant), somewhat loud (though there is often insulation), more polluting, and somewhat exotic to fix. Worse yet, despite the easier time finding fuel, turbines are about two orders of magnitude less efficient in mileage. While an AIC can optimize combustion to nearly 40 miles per gallon of methanol (17 Km per liter) turbines often get fractions of a mile to the gallon - though some complex machines use systems that will get two or three miles to the gallon.
It is fairly unlikely to find turbines in civilian vehicles due to the hot exhaust and low efficiency. Not impossible though, for example, turbine racing motorcycles were quite popular in the 40s. Military vehicles show somewhat more variety. Tanks with heavy weapons and many redundant electric motors driving the treads almost universally use turbines. Others depend on the manufacture - some will use fuel cells for weapons and A.I.C. units for moving, others will simply eschew high energy systems for missiles and conventional guns. Vehicles do not have nearly as many limits on storage capacity and weight as infantry, so a multi-task Gauss rifle is less needed when a normal fifty-caliber weapon will do.
Although range based on hydrocarbon fuel is usually the gold standard, Petrol is an extremely rare fuel at this point - both from peak oil, usage, and going stale from sitting. Plant based replacements - algae reacted bio-petrol, methanol, and ethanol are more common in liquid form. Hydrogen as seen some use, but only in areas near water and with plenty of electricity to produce on site - the economics of moving cryogenic liquid or very diffuse gas never really materialized.
In North America at least, there was no single solution to the problem of fuel production. Indeed, the faster and cheaper solution was to generally eliminate the need to travel and use fuel in the first place. Hence the presence of giant arcologies, fed by on site factories, with businesses manged through SPHERE augmented reality instead of on-site personnel. Even with multi-fuel vehicles, finding gas can be quite difficult.
Other Power Sources
Fuel cells are a quite common source of power. Although not always as efficient as batteries, in many applications, its quicker to refuel than recharge. Indeed, most major back-up systems now use such cells, since its easier to transport hydrogen or ethanol than car sized acid cells or four hundred degree thermal batteries.
Batter are rather common in cars. Often these are in the form of large packs on the underside of the car, designed to be swapped out with the right equipment. Rather than the vehicle remaining stationary for long periods of time while charging, the batter is replaced in a matter of minuets, and the old cell is then plugged in. These 100 kilo batteries have found a number of uses in the zone, even when the cars no longer function.