WalterC

Disconnect all but one sensor. If the sensor is externally powered, disconnect the laptop power supply. Doing this should produce a suitable measurement. Next, reconnect the laptop power supply and check for drifting. If it does, you could be looking at a ground loop. If it doesn't, connect another sensor and test for drifting. For minor ground loops, differential inputs are preferred over single-ended.

The USB-2627 input impedance is 1 G ohm and changing it is not possible. Instead buffer the signal. Use a voltage-follower op amp configuration to change your high impedance signal to low impedance. 
The board also uses analog multiplexers to expand the number of channels. High impedance signals will cause cross talk between channels and this could explain what you're seeing. A trick some use is to turn on an empty channel (connected to ground) after each high impedance connection. 
 

When measuring voltage with analog input ACH0 and ACH1 using USB-2627 and DAQami, the measured voltage will not match the actual voltage.
Is it possible to change the input impedance of analog input on DAQami?
If possible, could you please tell me the command? Or can I do that using UL and InstaCal?
I think this phenomenon is caused by installing voltage dividing resistors of 300kΩ and 100kΩ to reduce the voltage to a quarter before inputting it. By inputting 1V into this, I can see the following:
Voltage at the connector end of the channel containing the voltage dividing resistor: Measured about 0.7V Measure voltage of channel without voltage dividing resistor: 1V From this phenomenon, I inferred that the input impedance of the analog input port was low.

Hello @WalterC.
We recommend you short the inputs to unused channels if those channels are sampled, or to configure your software program to not sample from channel numbers which are open.  Most A/D daq devices have high input impedance front ends that, when left open, are likely to drift towards plus or minus full scale.  However, several MCC models (i.e. USB-1208LS, USB-1208FS, USB-1408FS, miniLAB 1008) have a resistive front end designed to divide down larger voltages and bias/shift from bipolar to unipolar, which results in a rather steady 1.4 volt reading when nothing is driving the input.  Ignore this value if sampling an open channel.
An additional bit of information is that these specific models work best for measurements, when connected to a low output impedance source.  If your signal has higher output impedance, such as a voltage divider or potentiometer output would have, inaccuracies will result.
Therefore, the 1.4 V reading is expected on an open channel.  If the other channels (not listed in your post) do not measure a 1.4 V reading, when left open, then verify various voltage levels connected to those channels.  Lastly, the USB-1408FS is no longer serviced by the factory, nor can a user service it in the field. 
Regards,
Fausto