Can we use liquid hydrogen to power a conventional engine?
The efficiency that matters is the efficiency of the vehicle not the efficiency of the engine

The problem of designing more efficient transport is bigger than the problem of designing better engines. Conventional combustion engines can be adapted to burn a wide variety of fuels (alcohols, natural gas and hydrogen are not too big a challenge). And there are alternative ways to move vehicles than combustion engines (fuel cells, for example, which run on hydrogen). So it looks like we can solve the engine problem.

But that isn't enough. To have a viable vehicle we have to solve other problems as well. How to store and deliver the fuel to the engine, for example. And how to distribute the fuel across the country so vehicles can be refilled. The second problem is probably easier to solve if the first problem–a viable vehicle–has a solution. Unfortunately, it isn't that easy.

To have a hydrogen powered car we would need a way to store enough hydrogen in the vehicle to allow it to drive several hundred miles. 

This is easy to do with liquid hydrocarbon fuels in conventional vehicles (petrol/gasoline and diesel have very high energy densities and can be stored in a simple unpressurised tank). The weight of the fuel alone is larger then the weight of the tank that contains it and the volume is small as the energy density is very high. 

It isn't so easy with hydrogen. While there are several existing ways to store hydrogen and some proposed solutions that are not yet operational, all of them involve big issues with volume and weight. Compressed hydrogen will involve very heavy thick-walled tanks and even then the energy density of the hydrogen gas alone will be lower than a tank full of petrol. The weight and volume of the tanks required to store as much energy as a tank of petrol will very large. Liquid hydrogen has a different set of compromises but isn't much better as it requires cryogenic system to keep the liquid hydrogen cool. There is considerable interest in clever chemical ways to store hydrogen (clathrates, metal organic frameworks and various molecular systems than can reversibly store hydrogen are all being researched).

To get an idea of the scale of the challenge it is worth looking at the mass and volumetric characteristics required to compete with conventional fuel. Diesel (slightly more efficient than petrol) carries about 12kWh/kg and about 10kWh/L. The current targets for research on hydrogen storage for the Fuel cell Technology Office are 1.5kWh/kg and 1kWh/L. This is about 10 times worse than diesel even ignoring the fact that fuel-cell power vehicles might have other advantages partially compensating the overall vehicle when compared to combustion engines. And the best technology solutions are much better than liquid hydrogen storage.

So you can use liquid hydrogen (or other ways of storing hydrogen) to power an conventional engine or vehicle (and such vehicles exist). But the cost and design compromises to make this work for a whole vehicle given that you need 10 time the volume and weight to store the equivalent energy, make such solutions not competitive for mass market vehicles.