The short answer is it all has to do with impedance matching. Regardless of what your sensor’s output impedance is, your DVM’s input impedance is probably around 10 Meg Ω or greater, and the input impedance of the USB-1208LS/FS or USB1408FS is only around 140 KΩ.
When you use your meter to measure the voltage coming out of your sensor, you are basically putting about a 10 MΩ resistor in parallel with your sensor's output resistor, which is very small say on the order of about 500 Ω. Your meter’s input impedance (or resistance) is so large that when seen in parallel with 500 Ω it does not affect the circuit and therefore does not affect the reading.
When you use a USB-1208LS/FS or USB-1408FS in the same scenario as above, and depending on the range you have it set to, you are putting about a 140 KΩ resistor in parallel with your sensor’s output resistor. Your USB-1208LS/FS or USB-1408FS’s input impedance (or resistance) is much lower than the DMV’s. When it is seen in parallel with 500 Ω it does affect circuit and therefore does affect the reading by showing a lower voltage.
Those of you who did the math here will not agree with this conclusion. 140 KΩ in parallel with 500 Ω is not significant enough to distort the voltage drop across a 500 Ω load. This is true, there is more going on here, but I did say this is the short answer.
The longer answer has to do with the input circuit of the USB-1208LS/FS or USB-1408FS (let’s just call it the USB-1X08 from here to keep it simple), which looks something like this:
The additional resistors make it possible for this 5V, USB port powered device able to read signals with amplitudes much higher than 5V. It can read signals that have amplitudes up to ±20V. The down side is these resistors lower the input impedance of the overall front end of the input to about 140 KΩ.
"So how do I get around this?"
Good question. All you need to do is add a small circuit with a unity gain amplifier. I know that sounds complicated, but you can get most of the parts from your local Radio Shack ® or other electronics parts distributor.
For each input channel you need to adjust, add the following circuit between your sensor and the input to the USB-1X08:
Where V+ is the power you supply to power the LM741 that needs to be no lower then the maximum signal outputting from the sensor so you do not clip it. V- is the negative power you supply to the LM741 that needs to be no higher than the minimum signal you are outputting from the sensor so you do not clip it.
Of course the LM741 is not the only choice here. It is actually an older design amplifier, but easy to find and get. It has some other benefits as well. It comes in a wide variety of packages such as DIP or Dual In line Package for through hole mounting or surface mount, etc. It even comes in a quad package. You can also use OP07, AD8675 or AD8510. In short, there is a wide variety of general purpose operational amplifiers you can use to resolve this.
http://www.national.com/an/LB/LB-42.pdf