The chlorate system is very complex. I doubt that the open-circuit potentials can be actually measured in solution, but rather are calculated from heats of formation. If the term "oxidizing strength" is used to compare systems, it should be rigorously defined; in this case, it seems that "oxidizing strength" is defined as "open-circuit voltage". But this could be a poor definition - even woefully poor.
In particular, the comparison of the open-circuit voltages does not include the potential current derivable from the reaction of a mole of each oxychloride. The output energy of the electrolytic cell (if you could just test each reaction, one at a time) would be the output voltage times the number of electrons transferred. By that standard, perchlorate will consume 7 times as many hydrogens as hypochlorite, and thus give 7 times as much current, with only a slightly lower voltage.
A comparison of the heats of reaction (just for the acidic equations) proves to be much more dramatic:
2 moles hypochlorous acid (total heat of formation = -56 kcal (CRC Handbook) produces 2 moles of H2O (total heat of formation = -136 kcal)
2 moles chlorous acid (-28 kcal) --> 4 moles H2O (-272 kcal)
2 moles chloric acid (-46 kcal) --> 6 moles H2O (-362 kcal)
and 2 moles perchloric acid (-62 kcal) --> 8 moles H2O (-544 kcal).
The heats of formation of the chlorine acids are similar, but the heat of the reactions is much higher for the more highly oxidized acids.
A mental picture using water: imagine 4 dams each 200 feet high and 200 feet wide. The lake behind the first is filled with water 163 feet deep and is 2 miles long. The second lake is 164 feet deep and 6 miles long. The third is only 147 feet deep, but 10 miles long. The fourth is 142 feet deep but 14 miles long. A pressure gauge at the dam would indicate the height (similar to the open circuit potentials above), but if the dam is used to provide power, the fourth dam/lake will outshine the other three.
Assuming that all the electrons don't react simultaneously, the open circuit potentials are a measure of the activation energy of the first step of the overall redox reaction: in order to get zero current, you just have to stop the first step. This activation energy will be sensitive to many factors, and we occasionally oversimplify, ignoring the succeeding steps by using non-quantitative words like "strength". The total oxidation strength will be a combination of all these steps, and the open circuit potential may not reflect this combination.