Why is the efficiency of human cells less than the efficiency of an Otto engine?
Can we compare alive cells with heat engines at all?
No, not really, because the living being isn't only a heat engine. There are three main points I want to make here.
1. Homeostasis Requires Constant Energy Input
This statement is especially true and obvious of homeotherms Mammals (Mammaliaformes, descended from the Therapsid Synapsid Amniotes), and Birds (Avialae / Dinosauria, descended from Dinosauriform Amniotes), which use a great deal of energy simply keeping their body temperature within strict limits, i.e. compensating for (mainly convective) heat loss from their body in cold conditions and actively expelling heat from their bodies in hot conditions. But, more generally, the phenomenon of homeostasis also requires expenditure of energy; a living organism is a highly non-equilibrium thermodynamic system, and excess entropies produced by metabolic processes must be expelled to keep it that way. Thermodynamic equilibrium is only reached when the living creature dies.
From this consideration alone, we would expect efficiencies measured when the organism does mechanical work to be considerably less than those of a heat engine.
2. Muscular Action is Not a Heat Engine
Muscular action is much more comparable to an electric motor than a heat engine. What I mean by this is an electric motor converts essentially work from one form to another with near to zero entropy change and negligible temperature change; motor proteins convert low-entropy energy stored as ATP to mechanical work through the hydrolysis of ATP with very small temperature change in the reagents as they react. In this case, the most meaningful measure of efficiency is probably expressed in two factors: (1) the ratio of the free energy $\Delta G$ of the ATP hydrolysis reaction to the total enthalpy change $\Delta H$ of the reaction (the difference $T\,\Delta S$ being the work we have to "give up" to expel the excess entropy of the reactants relative to lower entropy reaction products) and (2) the ratio of the mechanical work done to the available $\Delta G$.
In a heat engine, we take a quantity of heat from a hot reservoir, reducing the latter's entropy by $Q_i/T_i$ in the process, but find that, if we have a colder reservoir at $T_o<T_i$ we only have to "give back" $Q_o<Q_i$ to the cold reservoir to offset the entropy drop in the hot reservoir, so we get to "keep" energy $Q_i - Q_o > 0$ for doing work with. In biological reactions, the most comparable process to this is that of photosynthesis, where the "working fluid" of light at thermodynamic equilibrium at $6000{\rm K}$ is converted to "stored work" in sugars and, ultimately, ATP, dumping excess heat at ambient temperature $300{\rm K}$ in the process. Thenceforth, all living things use this low-entropy energy store rather like an electric motor converting energy stored in a capacitor, whether it be plants using it for their own life process, or herbivores accessing it through eaten plants or carnivores accessing it through eaten plant eaters.
So the plants and their solar energy fixing are the component of the biosphere most comparable to a heat engine in a power station; the plant metabolic processes and animals that eat plants and each other to get access to stored energy in plants are more like the electrical appliances that use the work extracted by the power plant, with very little temperature change.
3. Proteins Denature at Roughly $50{\rm C}$
For any animal process that could be considered to be like a heat engine, the maximum intake temperature can be at most a few or at most a few tens of degrees kelvin above ambient. This is because biological machinery is fatally damaged by temperatures much higher than $40{\rm C}$. Proteins denature and lose their vital life functions at very low temperatures. So if there are any processes in life that can be thought of as reasonably analogous to heat engines, we would foresee their efficiencies to be very low, since the theoretical efficiency is of the order of $3\%$ given this limit.
An interesting exception to my point 3 comes up in deep sea life living near hydrothermal vents. John Rennie writes:
Re the last point, the efficiency could of course still be 100% if animals had a heat sink at absolute zero. It's the fact there is a very limited temperature difference available that matters, rather than the limited source temperature. Note also that some extremophiles are quite happy living in near boiling water.
so we have creatures dwelling in $100{\rm C}$ and over environments and the opportunity to dump heat into the surrounding sea at much lower temperatures. However, my understanding is that these creatures still use the chemical energy from what they can extract from the volcanic vents, rather than working as heat engines taking advantage of the temperature drop.
Why is the efficiency of human cells less than efficiency of an Otto engine?
It's not. You are comparing two very different things. The low value of 18 to 26% efficiency you found for the human body is the energy produced by an exercising human compared to the energy consumed by that person. The high value of 56 to 61% efficiency is for an ideal Otto cycle engine. You need to compare apples to apples.
Can we compare alive cells with heat engines at all?
In a sense, no, for the simple reason that cells are not heat engines. However, in the sense that thermal efficiency is the ratio of usable energy produced during a cycle to total energy (usable energy plus heat losses), one one can compute the ratio of usable energy produced during a muscle cell contraction / retraction cycle to the chemical energy consumed by that cell in performing that cycle. These efficiencies are comparable numbers.
There are plenty of published papers on this topic. For example, see Sharon Jubrias, et al., "Contraction coupling efficiency of human first dorsal interosseous muscle." The Journal of Physiology 586.7 (2008): 1993-2002, which finds that the muscles in a human hand are about 68% efficient. Also see Nathaniel's answer to the physics.SE question "Human as a heat engine".
The cells in a human body need to be quite efficient to obtain that apparently low value of 18% to 26% efficiency while exercising. There's a lot of energy consumption occurring in a human body in addition to the leg muscles used to power a bicycle. A certain amount if energy is needed just to keep every cell in the body alive. This includes the human brain, which consumes about 20% of this resting energy. The elevated energy consumption while exercising requires the heart to pump faster and your chest to breath faster. Those muscles are consuming extra energy while exercising but are contributing nothing to the work being performed.
Now let's look at an automobile. The 56 to 61% efficiency figure you cited is for an ideal Otto engine. The intake and power strokes in an ideal Otto cycle engine are adiabatic reversible processes. Those strokes are less than ideal in a real Otto engine reducing the efficiency considerably. An automobile has overhead costs, just as does the human body. Some of the energy produced by an automobile engine is used to create electricity and to power pumps and fans. Internal combustion engines lose yet more energy in the form of unburnt fuel in the exhaust, internal friction, and losses in the transmission.
The 18% to 26% efficiency figure is the system efficiency of a human body. When one looks at the system efficiency of an automobile, the ratio of the energy used to accelerate the car and push aside air to the energy consumed in the form of gasoline, it too is very low, in the single digits for city driving and low to mid teens for highway driving at non-excessive speeds.
Let's calculate engine efficiency by using the ratio of work and gasoline energy (assuming it can be completely converted to CO2 and H2O). And let's calculate cell (muscular) efficiency by the ratio of work (from gym equipment) and fat energy (assuming it can be completed converted to CO2 and H2O). These two efficiency are comparable.
A gasoline engine efficiency is about 30%. If the oil processing is included, it can be even lower. Cell efficiency 18-26% is not too low. The question might be where does the rest 82%-74% energy go? My thinking it can be used to accelerating circulation system (increase heart beating frequency, transporting material like oxygen etc) and it is used up as heat is removed from the body. A demographic plot should be a study topic for bio engineering scientists.