The resistance at 0V is, of course, the slope of the V-I curve at that operating point. For diodes that is essentially a leakage current measurement, since the junction isn't forward biased. Leakage current is small compared to the normal forward biased operating region and, at the device level, isn't a parameter that's well controlled. Note that there is no characterization at 0V in the
datasheet. This may be particularly true for an array of parallel diodes. Things like illumination or the actual junction temperature may cause significant differences.
Still, "tens of Ohms" does sound surprisingly low. Suppose your array was operated at 3.5V & 0.5A, then if there really was a 20Ω resistor in parallel with it, it would divert 175mA away from the junction, which would have a noticeable effect on the intensity. Diodes are very nonlinear, so you may want to think about why you need to measure the 0V parameters and what they mean for your application.
This is a case where you really shouldn't just assume that your multimeter will give you a meaningful answer, unless you understand how the meter is making it's measurements. For example, the bias current applied in most ohmmeters is dependent on the range, so the meter may be selecting different operating points and exaggerating differences.
Regardless of this particular problem, it is a good idea in any EE lab to get to know how your meter makes these measurements. This is easily done with a couple of DMMs measuring each other. No, they aren't all the same. I would use different DMMs in different circumstances depending on their individual quirks. Don't assume your instruments are "fool proof", they only appear that way when used in common applications. As soon as you see confusing results, like this one, you should look more carefully at how the measurements are actually being done. It wouldn't be too hard to build your own with a power supply, resistor, voltmeter, ammeter, and a calculator; then you'll know better how the device is actually being excited. A curve tracer would be great if you have access to one, or you could plot your own DC V-I curve by hand.